Abstract:
A waveguide of radio frequency electromagnetic fields is multi-furcated into a plurality of radio frequency waveguide sections, each radio frequency waveguide section having an optoelectronic modulator electrically coupled to it. Each optoelectronic modulator has an optical waveguide disposed therein such that, in use, light traveling in the optical waveguides of the optoelectronic modulators travels in a direction orthogonal with respect to the direction the radio frequency electromagnetic field travels in the radio frequency waveguide sections. The plurality of radio frequency waveguide sections are fed from a common source of said radio frequency energy. In some embodiments, each radio frequency waveguide section has a dielectric material having a length and/or a dielectric constant selected such that a relative time delay of the radio frequency energy propagating in the radio frequency waveguide sections accommodates for a time delay of the light traveling from one optoelectronic modulator to a next optoelectronic modulator of a series connection of multiple optoelectronic modulators.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is related to the following US patent applications: U.S. Ser. No. 12/141,825, filed on Jun. 18, 2008 and entitled “Optoelectronic modulator and electric-field sensor with multiple optical-waveguide gratings”; U.S. Ser. No. 12/141,834, filed on Jun. 18, 2008 and entitled “Enhanced Linearity RF Photonic Link”; U.S. Ser. No. 12/176,089, filed on the same date as this application and entitled “Parallel Modulator Photonic Link”; and U.S. Ser. No. 12/176,071, filed on the same date as this application and entitled “Microwave receiver front-end assembly and array”. The disclosures of each of these related applications are hereby incorporated herein by reference. 
     TECHNICAL FIELD 
     This application discloses a receiver front-end assembly that is sensitive to small radio frequency (RF) signal powers incident upon that assembly, yet is also resistant to damage caused by unwanted high power electromagnetic radiation. 
     BACKGROUND 
     The adverse effect of high-energy electromagnetic (EM) fields incident on communication radios has been known for a long time. The usual protection against such high field levels has either been fuses, spark gaps or component circuit breakers. Fuses, once activated, need to be replaced before the radio can operate again. Component circuit breakers such as semiconductor diodes or capacitive shunts and spark gaps are limited in the amount of current/voltage that can be shunted and by their reaction time. This disclosure describes a technique to make the front-end of a radio system tolerant of high-energy EM fields while also having high sensitivity to low-energy RF EM signals. One known way to sense incident EM radiation is to use an antenna that is electrically coupled to an electro-optic modulator. The electro-optic modulator is part of an RF-photonic link that also includes a laser light source and a photodetector. The electro-optic modulator modulates the intensity or phase of the light supplied to it from the laser according to the amplitude of the RF signal coupled to that modulator from the antenna. The modulated light from the electro-optic modulator is then supplied to the photodetector which converts that modulated light into an RF electrical output signal. One need of this approach is to achieve strong depth of modulation and good sensitivity to weak RF input signals. 
     A prior art technique for an electro-optic modulator uses a single optical waveguide formed in electro-optic material and an array of multiple modulator sections that are optically connected in series to increase the depth of modulation, as described by: James H. Schaffner and William B. Bridges, “Broad Band, Low Power Electro-Optic Modulator Apparatus and Method with Segmented Electrodes,” U.S. Pat. No. 5,291,565, Mar. 1, 1994. Each of the multiple modulator sections is driven by its own set of electrodes. This prior art disclosure uses printed circuit electrodes and a printed circuit delay structure to feed the input electrical signal to those electrodes such that a phase match is maintained between the RF signal and the optical signal at each electrode. These printed circuit electrodes, because of the high level of their fringing field, cannot withstand a high power RF input. In contrast, the present disclosure uses RF waveguides instead of printed circuit electrodes and printed circuit delay and feeding structure to supply and delay the RF drive signal to the modulators, in order to avoid damage from an incident high power electromagnetic pulse. 
     Another prior art electro-optic modulator with multiple electrodes that drive an optically series connection of modulator sections is described by: William B. Bridges, “Antenna-Fed Electro-Optic Modulator,” U.S. Pat. No. 5,076,655, Dec. 31, 1991. The multiple electrodes are electrically fed by means of the EM field propagating in an RF waveguide, with those multiple electrodes acting as multiple antenna elements that couple the EM field propagating in the RF waveguide. Those multiple electrodes of the modulator are physically separate from the metal walls or enclosure of the RF waveguide and no electrical current flows directly from the metal walls of the RF waveguide to those electrodes. In contrast to this prior art, the present disclosure uses modulators whose electrodes are physical and electrical extensions of the metal walls of the RF waveguide. Electrical current can flow directly from those metal walls to those modulator electrodes. Thus, unlike the prior apparatus of Bridges, the presently disclosed modulators do not have electrodes that are separate from the metal walls of the RF waveguide that feeds the RF signal to those modulators. 
     An example of arrays of electro-optic modulators whose electrodes also act as antennas is described by: Joseph E. Moran, “Apparatus and System for Imaging Radio Frequency Electromagnetic Signals,” U.S. Pat. No. 6,703,596, Mar. 9, 2004. This patent is for an imaging antenna array wherein each antenna element in the antenna array is connected to a separate electro-optic modulator. The apparatus of Moran uses multiple antenna elements and has a single modulator electrically coupled to each antenna element and physically located adjacent to that antenna element. Each antenna element also serves as a drive electrode for a modulator. In contrast, the present disclosure has multiple electro-optic modulators or modulator sections electrically coupled to each antenna element. These modulators or modulator sections can be located at some distance away from the antenna element, being coupled to the antenna element by means of RF waveguides. 
     The use of multiple parallel plate (TEM) RF waveguides in an array, as a multi-furcation of space, has been known for a long time. However, these prior art have been used for electric-field combining, for example in RF lenses. The difference between these prior art and the use of parallel plate RF waveguides in the present disclosure is that our parallel plate multi-furcation is used to feed RF voltage to an array of optical modulators. These prior art do not include this RF to optical conversion and do not include any optical modulators. The classical paper on the parallel plate lens is: J. Ruze, “Wide-Angle Metal-Plate Optics,”  Proceedings of the I.R.E ., Vol. 38, No. 1, January 1950, pp. 53-59. 
     The prior art also includes the following documents which are referenced herein:
     1a. NAVSYNC CW20 GPS receiver specification—www.navsync.com   1b. LINX Technologies RXM-900-HP-II RF Module specification—www.linxtechnologies.com   1c. MAXIM, “Receiver Sensitivity Equation for Spread Spectrum Systems, MAXIM application note 1140, Jun. 28, 2002, www.maxim-ic.com/an1140.   2. Dr. Lowell Wood, acting chairman for the Commission to Assess the Threat to the U.S. from Electromagnetic Pulse Attack, “Opening Statement before the United States Senate Committee on the Judiciary, Subcommittee on Terrorism, Technology and Homeland Security”, Mar. 8, 2005.   3. R. T. Lee and G. S. Smith, “A Design Study for the Basic TEM Horn Antenna,” IEEE Antennas and Propagation Magazine, Vol. 46, No. 1, February 2004, pp. 86-92.   4. A. K. Ghatak and K. Thyangarajan, Optical Electronics, Cambridge University Press, Cambridge, 1989, pp. 441-447.   5. Emerson and Cuming Microwave Products, Eccostock® HiK500F data sheet, www.eccorsorb.com, rev. May 11, 2007.   6. G. E. Betts, L. M. Johnson, and C. H. Cox, “High-Sensitivity Bandpass RF Modulator in LiNbO3,” SPIE Integrated Optical Circuit Engineering VI, Vol. 993, 1988, pp. 110-116.   7. J. W. Shi, C. A. Shiao, Y. S. Wu, F. H. Huang, S. H. Chen, Y. T. Tsai, and J. I. Chyi, “Demonstration of a Dual-Depletion-Region Electroabsorption modulator at 1.55-μm Wavelength for High-Speed and Low-Driving-Voltage Performance,” IEEE Photon. Technol. Lett., Vol. 17, No. 10, October 2005, pp. 2068-2070.   8. S. B. Cohn, “Optimum Design of Stepped Transmission-Line Transformers,” IRE Trans. Microwave Theory Tech., Vol. 3, No. 3, April 1955, pp. 16-20.   9. K. Morito, S. Tanaka, S. Tomabechi, and A. Kurmata, “A Broad-Band MQW Semiconductor Optical Amplifier with High Saturation Output Power and Low Noise Figure,” IEEE Photon. Technol. Lett., Vol. 17, No. 5, May 2005, pp. 974-976.   

     Many of today&#39;s sophisticated communication radio receivers are extremely sensitive and need to demodulate signals that are well below −100 dBm, that is, less than 100 fW (see documents 1a-1c mentioned above). While this low signal threshold increases the range between the transmitter and the receiver, it also makes these receivers highly susceptible to destruction by high power incident radiation. These high power incident radiation can be caused on purpose (see document 2 mentioned above), or could even be accidental (e.g. from crossing the path of a high power microwave beam). The invention described in this disclosure addresses the need to maintain high radio sensitivity, while at the same time insuring tolerance to transient high power electromagnetic radiation. 
     In order to understand the ability of the disclosed receiver front-end assembly&#39;s capability to withstand high power microwave or RF radiation while maintaining high sensitivity, consider the single element  10  shown in  FIG. 1 . This element is described in greater detail in the related U.S. Ser. No. 12/176,071, filed on the same date as this application and entitled “Microwave receiver front-end assembly and array” mentioned above, but is summarized here as background material for a better understanding of the present invention. A transverse electromagnetic (TEM) horn antenna  50  channels the RF signal into a TEM waveguide  25  in which one or more electro-optic modulators  20  are located. Although the horn antenna  50  needs not be TEM, it is important that the waveguide  25  be TEM in order to establish as uniform a transverse electric field as possible across an electro-optic modulator  20  embedded in the waveguide  25 . An optical signal from a laser (not shown) interacts with the RF signal inside the width of the TEM waveguide  25  (see document 4 noted above) resulting in modulation of the phase or intensity of that optical signal. Other antennas besides horn antennas could be used as long as they have appropriate transitions to the TEM waveguide  25 . The waveguide  25  is preferably filled with a dielectric material whose relative permittivity (or dielectric constant) has a value that is close to the permittivity of the material from which the electro-optic modulator  20  is fabricated. For example, if the modulator  20  is fabricated from lithium niobate (LiNbO3), the required dielectric constant should be approximately thirty. This can be achieved using ceramic based material such as Emerson and Cumings Eccostock (see document 5 noted above). The reason for this constraint is so that there is little reflection at the interface between the RF waveguide and the electro-optic modulator(s). The TEM waveguide  25  may be terminated in a high power load or another TEM waveguide  26  or TEM horn  70 , or may even not be terminated. 
     The electro-optic modulators  20  have integrated optic waveguides, but have no printed circuit electrodes, which makes them quite a bit different than other prior art integrated optic modulators, such as those described in document 6 noted above. This avoidance of printed circuit electrodes is to prevent the electric field across an individual integrated optic waveguide from becoming too high during exposure to a high power electromagnetic pulse, which could produce a fringing electric field so high as to cause the dielectric material nearby the integrated optic waveguide to breakdown. With the assembly of  FIG. 1 , the electric field is maintained between the two pieces of metal that make up the top and bottom conductors  53  of the TEM waveguide. Because the depth of modulation of the optical signal in the electro-optic modulator is directly proportional to the electric field strength, the modulation is weakened by the need to keep the top and bottom conductors of the TEM waveguide far apart. Sufficient distance must be kept between those top and bottom conductors to avoid breakdown of the dielectric fill material and of the electro-optic material when that assembly is exposed to the high power electromagnetic pulse. Note that the fringing fields produced in a TEM waveguide can be significantly lower than the fringing fields produced at a printed circuit electrode. 
     In order to improve the sensitivity of the front-end assembly to weak input electromagnetic signals one can use some combination of multiple electro-optic modulators. One way to combine multiple modulators is to cascade those modulators, as described in related U.S. patent application Ser. No. 12/141,825, filed on Jun. 18, 2008 and entitled “Optoelectronic modulator and electric-field sensor with multiple optical-waveguide gratings”. Another way to combine multiple modulators is to arrange them optically in parallel but feed them from the antenna electrically in series, as described in related U.S. patent application Ser. No. 12,176,089, filed on the same date as this application and entitled “Parallel Modulator Photonic Link”. The optical outputs from these multiple parallel-arranged modulators are combined to produce a stronger output signal. The approaches described in these two related patent applications make use of multiple modulators that are formed within and electrically coupled to the same TEM RF waveguide. In contrast, the multiple modulators disclosed herein are electrically coupled to different RF waveguide portions of the multi-furcation. Those multiple modulators also may be formed exterior to the RF waveguide portions and attached to the ends of those RF waveguide portions. Preferably, those multiple modulators are formed on the same electro-optic modulator substrate. 
     BRIEF DESCRIPTION OF THE INVENTION 
     The disclosed assembly uses a linear array of optoelectronic modulators that are electrically coupled to a linear array of RF waveguides, an example of which is a dielectric filled TEM waveguide. The optical signals in the modulators travel in a direction orthogonal to the direction an RF signal travels in the RF waveguide. Each RF waveguide is part of a multi-furcation of a larger RF waveguide that is fed by a single antenna, such as a TEM horn, a dielectric rod or a dish. For a TEM RF waveguide, the top and bottom walls of the TEM waveguide are electrically coupled to the electrodes for the modulators. In one embodiment, modulators in the array can be optically connected in series, or be cascaded, so that the optical signal travels in sequence from one modulator to the next in the array. The depth of modulation can then be enhanced by using different electrical lengths for the RF waveguides feeding the RF signals to different ones of the modulators in the array, in order to keep the RF signal driving the modulation of those modulators phase matched to the modulated optical signal that propagates from one modulator to the next. A single output optical fiber then connects the assembly with the photodetector of the RF-photonic link. In an alternative embodiment, the modulators in the array can be optically connected in parallel such that each modulator receives an unmodulated optical signal from its laser source and each optical signal is modulated the same way by the RF signals supplied in parallel by means of the multi-furcation. These optical signals may come from one or more lasers, and may be at the same or different wavelengths (the general use of parallel optical modulators is described in related U.S. patent application Ser. No. 12/176,089, filed on the same date as this application and entitled “Parallel Modulator Photonic Link”. The overall optical link gain is increased because the modulated optical signals from the parallel modulators are detected by one or more photodetectors and summed. 
     The novel features of this invention include:
         A TEM waveguiding structure that is multi-furcated into an array of reduced height TEM waveguides and an array of electro-optic modulators whereby each electro-optic modulator is electrically coupled to a reduced height TEM waveguide.   A multi-furcated TEM waveguiding structure where each reduced height TEM waveguide is dielectrically loaded such that the time delay of the signal within each reduced height TEM waveguide can be controlled. This control can be achieved using different lengths of dielectric in different TEM waveguides or by using different materials in different TEM waveguides, with those different materials having different values for their relative permittivity or dielectric constant.   An embodiment wherein each modulator is connected optically in series to provide enhanced modulation sensitivity and a single optical output is connected to the radio receiver. This embodiment includes a method of establishing the delay or electrical length of each reduced height TEM waveguide so that the RF signal and the modulation of the optical signal remain phase matched throughout the assembly.   An embodiment wherein each modulator is connected optically in parallel with optical inputs provided from one or more laser sources. The parallel optical outputs lead to one or more photodetectors at the receiver, where the detected RF carriers are electronically summed to provide an enhanced signal magnitude.   Each reduced height RF waveguide of the multi-furcation includes an impedance matching structure. A separate matching structure may be located within each reduced height waveguide of the multi-furcation, or a single matching structure may be located before the multi-furcation and cover the entrance to all of the reduced height waveguides.   Use of optical amplifiers between cascaded modulator sections to maintain a high optical modulation response at each modulator section.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a single element of the microwave receiver front-end assembly of the type disclosed in related U.S. Ser. No. 12/176,071, filed on the same date as this application and entitled “Microwave receiver front-end assembly and array”. 
         FIGS. 2   a  and  2   b  respectively depict side-elevation and top views of an embodiment of the invention having optically parallel-connected modulator sections. A single modulator substrate containing the multiple parallel-connected optical modulators is shown, wherein each modulator is electrically coupled to a separate reduced height RF waveguide of the multi-furcation. The metal walls of the multi-furcation also serve as electrodes for each modulator. Each modulator has a separate optical input and output and the parallel modulated optical carriers are detected at the receiver. 
         FIGS. 2   c  and  2   d  respectively show side-elevation and top views of another embodiment of the invention having optically parallel-connected modulator sections. A single modulator substrate containing the multiple parallel-connected optical modulators is shown, wherein each modulator is electrically coupled to a separate reduced height RF waveguide of the multi-furcation. The multiple modulators are optically connected to a set of integrated optic waveguides at each of the two ends of the modulators. 
         FIGS. 2   e  and  2   f  respectively show side-elevation and top views of another embodiment of the invention having multiple optically parallel-connected modulators, wherein each modulator is electrically coupled to a separate reduced height RF waveguide of the multi-furcation. The physical spacing between the reduced height RF waveguides increases gradually from the point of the multi-furcation to their intersection with the modulator substrate containing the multiple modulators. 
         FIG. 3  provides an exploded view of two reduced height waveguides of the multi-furcation and the two modulators that are electrically coupled to those reduced height waveguides. 
         FIG. 4  depicts a front-end assembly having either a physically separated antenna such as a dish antenna or having no other antenna and the RF signal couples directly to the multi-furcation through the impedance matching structure. 
         FIG. 5  depicts a front-end assembly having a physically separated antenna such as a dish antenna that focuses and couples the RF signal into a multi-furcated RF waveguide, such as a set of multiple parallel TEM waveguides, that are electrically coupled to multiple optoelectronic modulators on a modulator substrate. 
         FIGS. 6   a  and  6   b  are respectively side-elevation and top views of another embodiment of the invention having multiple optically parallel-connected modulators, wherein each modulator is electrically coupled to a separate reduced height RF waveguide of the multi-furcation. The multiple modulators are optically connected to a set of integrated optic waveguides at each of the two ends of the modulators. 
         FIG. 7  shows a side view of another front-end assembly that has either a physically separated antenna such as a dish antenna or no other antenna, with the RF signal coupling directly to the multi-furcation through the impedance matching structure. The spacing between the multiple reduced height waveguides of the multi-furcation increases gradually from the point of the multi-furcation to their intersection with the modulator substrate containing the multiple modulators. 
         FIG. 8  depicts an embodiment of the invention comprising an array of optoelectronic modulators on a modulator array substrate, wherein the multiple modulators of that array are each electrically coupled to a different dielectric waveguide portion of a multi-furcated dielectric waveguide. The multi-furcated dielectric waveguide is further electrically and physically coupled to a pyramidal dielectric rod antenna. 
         FIGS. 9   a  and  9   b  are respective side elevation and top view of an embodiment of the invention comprising a single modulator substrate containing an optically series-connected array of optoelectronic modulators that are electrically coupled to a multi-furcated (trifurcated in the figure) TEM waveguide wherein each waveguide furcation has an appropriate electrical length to time match to the optical signal modulated by the RF signal supplied through that branch. 
         FIG. 10  depicts another embodiment of the invention wherein the RF time delay progression is caused by using different dielectric materials, with differing values of their relative permittivity, in different ones of the multiple reduced height waveguides of the multi-furcation. 
         FIG. 11  is a top view of a single modulator substrate containing a series-connected array of modulators electrically coupled to a multi-furcated (trifurcated in the figure) TEM waveguide, such as shown in  FIG. 9 , but wherein one or more of the optical waveguides interconnecting the series-connected modulators includes an optical amplifier to provide a more uniform level of the optical carrier signal supplied at the entrance of each modulator of the series-connected array of modulators. 
         FIG. 12  depicts an array of horn antennas wherein each horn is connected to a separate multi-furcated RF waveguide and optical modulator substrate. The optical signals entering multiple optical modulator substrate could be supplied from a single laser that is multiplexed into each element or could be supplied from multiple lasers. The output modulated optical signals are collected by the radio (not shown) for processing into various antenna-beam pointing directions. 
         FIG. 13  depicts an array of RF front-end assemblies having multi-furcated waveguides electrically coupled to multiple modulators on a modulator substrate, wherein parallel optical signals are modulated by parallel optical modulators for each element of the array. 
         FIG. 14  depicts an embodiment of the invention comprising an array of optoelectronic modulators that are electrically coupled to a multi-furcated (trifurcated in the figure) TEM waveguide containing multiple reduced height TEM waveguides. The multi-furcated TEM waveguide is further electrically and physically coupled to a dielectric rod antenna. 
     
    
    
     DETAILED DESCRIPTION 
     A first embodiment of this invention wherein multiple optoelectronic modulators are coupled to a single antenna or antenna element is shown in  FIGS. 2   a  and  2   b . In these figures, a horn antenna  50  feeds an incident RF electromagnetic signal  60  into a transverse electromagnetic (TEM) multi-furcated RF waveguide  25   in  (the depicted waveguide is trifurcated, but may have as large a number of furcations or branches as desired). The multiple TEM waveguide sections, i.e., the reduced height TEM waveguides  25 - 1  through  25 - n  of the multi-furcated waveguide  25  guide the RF EM field to a modulator substrate  22  that has an array of modulators, or modulator sections,  20 - 1  through  20 - n  that are physically oriented parallel to each other. Each modulator  20 - 1  . . .  20 - n  contains an optical waveguide  23 - 1  . . .  23 - n . Each modulator also could include an optional grating  29 . Each modulator  20 - 1  . . .  20 - n  is electrically coupled to an associated reduced-height RF waveguide  25 - 1  . . .  25 - n . Each reduced height RF waveguide  25 - 1  . . .  25 - n  supplies the RF signal for modulating the light in its associated optoelectronic modulator  20 - 1  . . .  20 - n . In general, a wide range of optoelectronic modulator types can be used, both electro-optic (see document 6 identified above) and electro-absorptive (see document 7 identified above), as long as the top and bottom metal sides  53 ,  53   i  of each reduced height waveguide  25 - 1  . . .  25 - n  acts as an electrode for the associated modulator element  20 - 1  . . .  20 - n.    
     In this embodiment, the optical connections or fibers  51 ,  52  to the optical waveguides  23 - 1  through  23 - n  of the modulator sections  20 - 1  through  20 - n  are made in parallel, with unmodulated light being coupled into each optical waveguide  23 - 1  through  23 - n  and modulated light being coupled from each optical waveguide  23 - 1  through  23 - n  to one or more photodetectors at a receiver  56 . The unmodulated optical inputs into each modulator section  20 - 1  through  20 - n  can be supplied by optical connections or fibers  51  from a single laser by using an optical splitter, known in the art, to split the optical signal into parallel parts, or the unmodulated optical inputs can alternatively be supplied from multiple lasers. The optical signal in each modulator section  20 - 1 , . . . ,  20 - n  is modulated by the RF electric field present in each reduced height waveguide  25 - 1 , . . . ,  25 - n  of the multi-furcated input waveguide  25 in, at the junction of the reduced height waveguide with the modulator substrate  22 . An optional output RF waveguide  26 out can similarly be multi-furcated. The modulated optical signal out of each modulator section is transmitted by optical fibers  52  or by free space optics to a receiver  56  that contains one or more photodetectors that convert the modulated light into an output RF signal. If the optical carrier from each modulator section is at the same optical wavelength, then an array of photodetectors is used, with a separate photodetector for each of the multiple modulators  20 - 1  through  20 - n . The RF signals output from the multiple photodetectors can then be summed by using known RF power combining techniques to enhance the overall modulated signal. If the optical carrier from each modulator is at a different optical wavelength or if each optical carrier is produced by a different laser, then a single photodetector can be used if a known optical power combiner is used before the receiver. The receiver processing of the parallel optical channels is preferably identical to that described in U.S. patent application Ser. No. 12/176,089, entitled “Parallel Modulator Photonic Link”, although in that application, the RF signal is not split into parallel reduced height waveguides. If the RF signal is expected to come from a direction normal to the horn aperture, or if that horn aperture and RF waveguide can support only the lowest-order waveguided mode, then the dielectric materials that fill the reduced height waveguides of the multi-furcation preferably have the same relative permittivity so that no difference in time delay is produced for the various RF signals arriving at the multiple modulators. All of the modulators thus are driven by the same temporal portion of the RF input signal  60  supplied to the antenna  50 . 
     This invention has utility in enabling one to sense the EM field energy incident upon a larger cross-sectional area of the front of the TEM waveguide. This need to sense a larger cross-sectional area may arise when the minimum allowable separation distance between the metal walls of the TEM horn  50  is limited by the need to keep the maximum level for the RF electric field at the entrance to the TEM waveguide  25 , for some specified high-power incident EM radiation, sufficiently low that the materials comprising the front end assembly will not exceed their dielectric breakdown strength. For example, assume that the horn antenna  50 , which could be one element of a phased array of horn antennas, feeds a single TEM waveguide  25  as depicted in  FIG. 1 . The lateral size of a typical optoelectronic modulator (suitable for light of 1550 nm wavelength) is on the order of 10 micrometers and multiple optoelectronic modulators typically can be placed side by side with a spacing of approximately 20-30 micrometers between their optical waveguides while remaining optically isolated from each other. If the front end must withstand very high power incident EM radiation, the minimum separation distance between the exterior metal walls  53  of the TEM waveguide  25  may need to be 100-200 micrometers or larger. Thus, much of the energy of an incident EM field would not be sensed if the TEM waveguide were coupled to only a single optoelectronic modulator. 
     In an optical or RF-photonic link with a single optoelectronic modulator that is driven by the RF signal supplied through a single TEM waveguide, the overall gain of the link, G 1 , is related to the voltage V 1  of the RF signal and the thickness or height d 1  of the TEM waveguide by 
     
       
         
           
             
               G 
               1 
             
             = 
             
               K 
               ⁢ 
               
                 
                   V 
                   1 
                 
                 
                   d 
                   1 
                 
               
             
           
         
       
     
     wherein K is a collection of constants that depend upon the other modulator and link properties [see document 11 cited above] such as the optical power into the modulator. In essence, the gain of the link is directly proportional to the magnitude of the electric field driving the optoelectronic modulator. For the case of the N-furcated TEM waveguide assembly with an array of N optoelectronic modulators, if the optical power supplied into each modulator of the array is the same as the optical power supplied into the original single modulator, then each of those N parallel modulators of the array contributes a gain G 1 ′ described by the formula below (where V 1 ′ is the RF signal voltage applied to the reduced height waveguide associated with that optoelectronic modulator and d 1 ′ is the thickness or height of the reduced height waveguide) 
     
       
         
           
             
               G 
               1 
               ′ 
             
             = 
             
               
                 K 
                 ⁢ 
                 
                   
                     V 
                     1 
                     ′ 
                   
                   
                     d 
                     1 
                     ′ 
                   
                 
               
               = 
               
                 
                   K 
                   ⁢ 
                   
                     
                       
                         V 
                         1 
                       
                       ⁢ 
                       N 
                     
                     
                       
                         d 
                         1 
                       
                       ⁢ 
                       N 
                     
                   
                 
                 = 
                 
                   
                     G 
                     1 
                   
                   . 
                 
               
             
           
         
       
     
     Therefore, if each of the modulated optical signals, or photodetected RF signals, is summed at the receiver, the total gain of the optical link is enhanced by a factor of N. 
     We provide an example of how to determine the minimum allowable separation between the two exterior parallel metal walls of a TEM waveguide, or to the height d 1  of a TEM waveguide, as well as to the height d 1 ′ of a reduced height waveguide of a multi-furcation. Assume that a high power RF signal with a power density of P 0  is incident at the entrance aperture of the TEM horn. If the entrance aperture of the horn were approximated as an open TEM waveguide, then the root-mean square voltage developed across that aperture would be 
     
       
         
           
             
               V 
               0 
             
             = 
             
               
                 
                   P 
                   0 
                 
                 ⁢ 
                 
                   Z 
                   0 
                 
               
             
           
         
       
     
     where Z 0  is the impedance of the TEM waveguide given by
 
 Z   0   =ηd   0   /w  
 
     and for which η is the free space wave impedance, 376.7Ω, d 0  is the distance between the metal top and bottom walls of the waveguide aperture and w is the width of the TEM assembly. Assume that this open TEM waveguiding horn transitions down to a separation of d 1  between its metal walls (or electrodes) without RF loss over a desired frequency band. Over these frequencies, very little power is reflected back out through the horn, so if we make the approximation that no power is lost, the ratio of the voltage at a point along the open TEM waveguiding horn to the voltage at the entrance aperture of the horn is 
     
       
         
           
             
               
                 V 
                 1 
               
               
                 V 
                 0 
               
             
             = 
             
               
                 
                   
                     Z 
                     0 
                   
                   
                     Z 
                     1 
                   
                 
               
               = 
               
                 
                   
                     
                       d 
                       0 
                     
                     
                       d 
                       1 
                     
                   
                 
                 . 
               
             
           
         
       
     
     Thus the voltage, V 1 , applied to the TEM waveguide coupled to the exit of the horn has been stepped up by the impedance transformation. If the height of the TEM waveguide is kept constant, and assuming negligible loss in the TEM waveguide, this voltage value also is applied across the optoelectronic modulator that is electrically coupled to that TEM waveguide. Now if the maximum allowable voltage is set to be the dielectric breakdown voltage, V BD , of some material, then the smallest value d 1  can have is 
     
       
         
           
             
               d 
               1 
             
             = 
             
               
                 
                   V 
                   0 
                   2 
                 
                 
                   V 
                   BD 
                   2 
                 
               
               ⁢ 
               
                 
                   d 
                   0 
                 
                 . 
               
             
           
         
       
     
     Now suppose the TEM waveguide coupled to the exit of the horn then transitions into N-furcated reduced height waveguides, with each reduced height TEM waveguide having a distance d 1 ′ between its top and bottom metal walls. Again we assume that there are no reflections over the desired operational band so that we can write 
     
       
         
           
             
               P 
               0 
               ′ 
             
             = 
             
               
                 
                   P 
                   0 
                 
                 N 
               
               = 
               
                 
                   
                     V 
                     0 
                     2 
                   
                   
                     NZ 
                     0 
                   
                 
                 = 
                 
                   
                     V 
                     1 
                     ′2 
                   
                   
                     Z 
                     1 
                     ′ 
                   
                 
               
             
           
         
       
     
     where V 1 ′ is the voltage across one reduced height waveguide of the N-furcation at its junction with the modulator. The impedance at the junction with the modulator is given by 
     
       
         
           
             
               Z 
               1 
               ′ 
             
             = 
             
               η 
               ⁢ 
               
                 
                   d 
                   1 
                   ′ 
                 
                 w 
               
             
           
         
       
     
     where w is the TEM waveguide width, which is assumed to be kept constant throughout the assembly. Thus, 
     
       
         
           
             
               V 
               1 
               ′2 
             
             = 
             
               
                 V 
                 0 
                 2 
               
               ⁢ 
               
                 
                   
                     d 
                     1 
                     ′ 
                   
                   
                     Nd 
                     0 
                   
                 
                 . 
               
             
           
         
       
     
     Also, 
     
       
         
           
             
               
                 V 
                 1 
                 ′ 
               
               = 
               
                 
                   V 
                   1 
                 
                 N 
               
             
             , 
           
         
       
     
     so 
     
       
         
           
             
               
                 
                   V 
                   1 
                   2 
                 
                 
                   N 
                   2 
                 
               
               = 
               
                 
                   V 
                   0 
                   2 
                 
                 ⁢ 
                 
                   
                     d 
                     1 
                     ′ 
                   
                   
                     Nd 
                     0 
                   
                 
               
             
             , 
           
         
       
     
     which means that when V 1 =V BD  we get an expression for the minimum spacing d 1 ′ between the metal walls of the reduced height TEM waveguide: 
     
       
         
           
             
               d 
               1 
               ′ 
             
             = 
             
               
                 
                   
                     V 
                     BD 
                     2 
                   
                   
                     NV 
                     0 
                     2 
                   
                 
                 ⁢ 
                 
                   d 
                   0 
                 
               
               = 
               
                 
                   
                     d 
                     1 
                   
                   N 
                 
                 . 
               
             
           
         
       
     
     Thus, d 1 ′ is smaller than d 1  by exactly the number of reduced height waveguides that make up the multi-furcation. 
       FIGS. 2   c  and  2   d  illustrate another embodiment of the modulator substrate  22 . Each of the reduced height TEM waveguides  25 - 1  through  25 - n  of the multi-furcated input waveguide  25   in  is electrically coupled to a different one of the optoelectronic modulators, or modulator sections,  20 - 1  through  20 - n . Those modulators  20 - 1  through  20 - n  are preferably all located on the same modulator substrate  22 . Although the minimum center-to-center spacing between those parallel arranged modulators can be as small as 20-30 micrometers, or even smaller, those multiple modulators may need to be optically connected to an array of optical fibers that supply the unmodulated light from the lasers and that carry the modulated light to the photodetectors of the link. A typical optical fiber for 1550 nm wavelength light has a diameter of approximately 125 or 250 micrometers. Thus, in order to accommodate the large center-to-center spacing between the arrays of optical fibers  51 ,  52  that connect to the multiple modulators  20 - 1  . . .  20 - n , the modulator substrate  22  may also contain optical-waveguide bends  24  in the optical waveguides  23 - 1  through  23 - n , as illustrated in  FIGS. 2   c  and  2   d , that make the transition from the wide waveguide-to-waveguide spacing that matches the optical fibers to the narrower waveguide-to-waveguide spacing permitted by the constraint to maintain optical isolation between the multiple modulators. 
       FIGS. 2   e  and  2   f  illustrate another way to accommodate the large spacing between adjacent optical fibers that couple to the multiple modulators on the modulator substrate  22 . In this case, the modulators have the same waveguide-to-waveguide spacing required by the size of the optical fibers. However, the reduced height TEM waveguides  25 - 1  through  25 - n  have curved or angled paths so that the center-to-center spacing between adjacent reduced height waveguides  25 - 1  through  25 - n  at the multi-furcation point of input waveguide  25   in  is small, constrained by the value for d 1 ′, but the spacing between those adjacent reduced height waveguides  25 - 1  through  25 - n  is larger at their junction with the modulator substrate  25 , constrained by the allowable spacing between optical fibers  51 ,  52 . In  FIG. 2   e , the TEM waveguides  25 - 1  through  25 - n  are depicted as touching a neighboring one or two of the TEM waveguides  25 - 1  through  25 - n  at their upper ends, but these TEM waveguides  25 - 1  through  25 - n  do not necessarily need to be in physical contact. They may be spaced apart slightly, for example at their upper ends, if desired. 
       FIG. 3  shows an exploded view of two adjacent reduced height waveguides  25 - 1  and  25 - 2  in the multi-furcation of input waveguide  25   in , and their locations relative to the two optical waveguides  23 - 1  and  23 - 2  of optical modulators  20 - 1  and  20 - 2 . The thin dielectric slabs that make up each TEM reduced height waveguide  25 - 1  and  25 - 2  could have metal coatings  53 - 1   a ,  53 - 1   b ,  53 - 2   a ,  53 - 2   b  deposited on the top and bottom faces of each slab. Adjacent slabs  25 - 1  and  25 - 2  could be electrically and physically attached together at those metal sides  53 - 1   b  and  53 - 2   a  that face each other, by having those metal sides  53 - 1   b  and  53 - 2   a  soldered together or bonded together with an electrically conductive epoxy. The optical modulator substrate  22  could have printed metal pads  27  that lie on either side of the optical waveguides  23 - 1  and  23 - 2 . These metal pads preferably are aligned with the metal coatings of the reduced height waveguides. These pads  27 , in turn, could be attached to the metal coatings  53  of the reduced height waveguide by means such as solder or conductive epoxy. The printed metal pads act as electrical extensions of the metal coatings  53 . Alternatively, the optical modulator substrate  22 , which generally is made of a dielectric or semiconducting material could have no printed metal pads but, instead, could be bonded directly to the reduced height waveguides  25 - 1  and  25 - 2 , with those reduced height waveguides aligned such that one metal coating  53  lies toward each side of an optical waveguide  23 - 1  and  23 - 2 . Finally, another set of reduced height RF waveguides  26 - 1  and  26 - 2  could, optionally, be attached to the back of the modulator substrate  22  to carry the RF power to an electrical-circuit load. If the modulator substrate  22  is connected to a second set of reduced height waveguides  26 - 1  and  26 - 2 , that modulator substrate also preferably has sets of metal filled or metal covered via holes  28  formed through it. Those via holes  28  preferably are aligned to the metal coatings  53  of both the first and second set of reduced height waveguides  25 - 1 ,  25 - 2 ,  26 - 1  and  26 - 2 . In this way, an electrical path is formed to conduct electrical current directly through the modulator substrate  22  from the first set of reduced height waveguides  25 - 1  and  25 - 2  to the second set of reduced height waveguides  26 - 1  and  26 - 2 . 
       FIG. 4  shows a different embodiment for which the entire aperture at the front of the assembly for coupling in the incident EM radiation  60  is filled with reduced height RF waveguides  25 - 1  . . .  25 - n . In this embodiment, an antenna element, such as the horn antenna shown in the preceding embodiments of  FIG. 2 , is not utilized for concentrating the incident EM field  60 . Instead, the incident radiation  60  is coupled directly into the furcated RF waveguide  25 . The incident radiation  60 , however, could be concentrated by means of a physically separate antenna such as the dish antenna  55  shown in  FIG. 5 . In the embodiment of  FIG. 4 , the multi-furcation can be considered to be part of an open ended RF waveguide  25  that has an aperture size equal to the aperture size of the horn antenna for the embodiment of  FIG. 2  (for example λ/2 for a scanning phased array) divided by the value of the dielectric constant of the dielectric material filling the reduced height waveguides. In  FIG. 4 , the input RF signal  60  couples directly into the multi-furcation  25   in  through the impedance matching structure  21 . This impedance matching structure  21  optimizes the coupling (minimizes the reflection) of the incident radiation  60  into the reduced height waveguides  25 - 1  through  25 - n .  FIG. 4  also illustrates that the reduced height waveguides  25 - 1  through  25 - n  need not be TEM waveguides, which have metal coatings or parallel metal plates covering the dielectric fill material, but those reduced height waveguides  25 - 1  through  25 - n  also could be dielectric waveguides, with no metal coatings, that are separated by gaps  27  having a lower value of their dielectric constant or relative permittivity compared to the dielectric material of reduced height waveguides  25 - 1  through  25 - n.    
       FIGS. 6   a  and  6   b  illustrate an embodiment of a dielectric waveguide structure  25  that comprises a multi-furcation of multiple closely spaced reduced-height dielectric waveguides  25 - 1  through  25 - n . These multiple reduced-height dielectric waveguides can be separated by gaps  27  that have a lower value for their dielectric constant than the value of the dielectric constant of the material of those dielectric waveguides  25 - 1  through  25 - n . A separate optoelectronic modulator  20 - 1  . . .  20 - n  of the multiple modulators on modulator substrate  22  is aligned to each of the reduced-height dielectric waveguides  25 - 1  . . .  25 - n  and senses the electric field propagating in that reduced height dielectric waveguide. In order to accommodate the large center-to-center spacing between an array of optical fibers  51 ,  52  that connect to the multiple modulators, the modulator substrate  22  may also contain optical waveguide bends  24  that make the transition from the wide waveguide-to-waveguide spacing matching the optical fibers  51 ,  52  to the narrower waveguide-to-waveguide spacing permitted by the constraint on the spacing between adjacent reduced height dielectric waveguides (e.g.,  25 - 1  and  25 - 2 ). 
     Alternatively, the dielectric waveguide structure  25  could be a single dielectric waveguide without any furcations or branches. That single dielectric waveguide  25  could be coupled to the modulator substrate  22  that contains multiple optoelectronic modulators  20 - 1  through  20 - n . In this case, the minimum spacing between adjacent modulators (e.g.,  20 - 1  and  20 - 2 ) on that modulator substrate  22  would be constrained by the need to maintain optical isolation between those adjacent modulators. The optical waveguide bends  24  would make the transition from the wide waveguide-to-waveguide spacing matching the optical fibers  51 ,  52  to the narrower waveguide-to-waveguide spacing permitted for adjacent modulators. 
       FIG. 7  illustrates a variation of the embodiment of  FIG. 4  for which the reduced height dielectric waveguides  25 - 1  through  25 - n  of the multi-furcated RF waveguide  25  have angled or curved paths. These dielectric waveguides  25 - 1  through  25 - n  are joined together at their end closest to the entrance of the multi-furcated structure, i.e., their end closest to the impedance matching structure  21 . The spacing between these dielectric waveguides  25 - 1  through  25 - n  is gradually increased so that the spacing when these dielectric waveguides are coupled to the modulator substrate  22  is the same as the spacing of the multiple optoelectronic modulators  20 - 1  through  20 - n  on that modulator substrate  22 . The reasons for having this increase in spacing are discussed above in relation to the embodiment of  FIGS. 2   e  and  2   f . When the reduced height waveguides  25 - 1  through  25 - n  are widely spaced the electric field presented to the multiple optoelectronic modulators  20 - 1  through  20 - n  may be reduced compared to the embodiments of  FIGS. 2   e  and  2   f  where the reduced height waveguides are implemented by TEM waveguides. An optional second set of reduced height dielectric waveguides  26 - 1  through  26 - n  couples the EM field, which was supplied by means of dielectric waveguides  25 - 1  through  25 - n , away from the modulator substrate  22  to a high power load. Also in  FIG. 7 , the waveguides  25 - 1  through  25 - n  are depicted as touching a neighboring one or two of the waveguides  25 - 1  through  25 - n  at their upper ends, but these waveguides  25 - 1  through  25 - n  do not necessarily need to be in physical contact. They may be spaced apart slightly, for example at their upper ends, if desired. 
       FIG. 8  illustrates another antenna that can couple incident RF radiation  60  to a dielectric waveguide multi-furcation  25 . This antenna is a dielectric rod antenna. The dielectric rod antenna  56  preferably has a pyramidal shape, with each side of the pyramid having a small width at its input end and with each side tapering to a much wider base at its junction with the dielectric waveguide  57 . The rectangular-shaped dielectric waveguide  57  then splits or branches into an N-furcated dielectric waveguide  25 , with each of the N-furcated dielectric waveguides  25 - 1  . . .  25 - n  having a reduced height compared with the dielectric waveguide  57  at the junction with the pyramidal rod antenna  56 . Each reduced height dielectric waveguide  25 - 1  . . .  25 - n  is then electrically coupled to a modulator  20 - 1  . . .  20 - n  located on the modulator substrate  22 . In this figure, the front end structure is shown as not having a second set of multi-furcated dielectric waveguide  26 - 1  through  26 - n . In this case, the EM field propagating in the multi-furcated dielectric waveguide  25  is reflected from bottom face of the modulator substrate  22 . This reflected EM field propagates again, in the reverse direction, through the entire structure and can exit through the antenna  56 . Although this figure shows the reduced height waveguides  25 - 1  through  25 - n  as being separated by gaps whose heights increase as those reduced height waveguides approach the modulator substrate  22 , the heights of the gaps could remain constant (as illustrated by  FIGS. 4   a  and  6   a ) or the gaps could have zero height. 
       FIGS. 9   a  and  9   b  depict another embodiment of the present invention which, as will be seen, has the reduced height RF waveguides coupled to multiple optoelectronic modulators, or modulator sections, that are optically connected in series, or that are optically cascaded.  FIGS. 10 through 12  show various modifications and adaptations of this serially connected modulator scheme. For these embodiments, the light to be modulated first passes through a first modulator and then through a second modulator and then through a third modulator, and so on. The modulation depth becomes increasingly greater as that light passes each successive modulator of the cascade. 
     In a first example of these embodiments, a large aperture TEM waveguide horn antenna  50  is shown (see  FIGS. 9   a  and  9   b ). This horn antenna  50  could have a minimum aperture dimension of one-half of a free space wavelength of the intended received signal  60 , and can be much larger. The horn antenna  50  may or may not be filled or loaded with a dielectric material. The horn antenna tapers down into a TEM waveguiding structure  25 . At the point where the taper reaches a minimum, it is connected to the TEM waveguiding structure  25 . At this point, the TEM waveguiding structure is multi-furcated (that is it has multiple branches) into multiple reduced height TEM waveguides  25 - 1 ,  25 - 2  and  25 - 3 . In this illustration, the input RF waveguide  25  is trifurcated into three reduced height waveguides  25 - 1 ,  25 - 2  and  25 - 3 , but it could be bifurcated or multi-furcated (with n waveguides). This multi-furcation is created by using metal plates  53 ,  53   i  that extend the width of the TEM waveguide. The outermost metal plates  53  of the multi-furcated waveguide are joined with (or integral with) the metal leaves  54  of the horn antenna  50 . A portion  37 - 1 ,  37 - 2 , and  37 - 3  of each reduced height waveguide of the multi-furcation is dielectrically loaded with a material that has a specific value for its dielectric constant ∈. These values could be the same or they could be different. Furthermore, the distance between the metallic plates  53 ,  53   i  bounding a dielectric-loading layer  37 - 1 ,  37 - 2 ,  37 - 3  of a reduced height waveguides  25 - 1 ,  25 - 2 ,  25 - 3  need not be the same as the distance between the metallic plates bounding the dielectric loading layer of a different reduced height waveguide. That is, the various reduced height waveguides  25 - 1 ,  25 - 2 ,  25 - 3  need not all have the same height. The use of a TEM waveguide  25  that is multi-furcated into multiple dielectric filled reduced height TEM waveguides  25 - 1 ,  25 - 2 ,  25 - 3  has the advantage of being able to maintain a uniform electric field strength over most of the width of each reduced height TEM waveguide  25 - 1 ,  25 - 2  and  25 - 3  of the multi-furcation. In order to transition efficiently from free space to the dielectrically loaded reduced height waveguides  25 - 1 ,  25 - 2 ,  25 - 3 , impedance matching structures  21 - 1 ,  21 - 2 ,  21 - 3  are included as shown in  FIGS. 9   a  and  9   b  adjacent each waveguide  25 - 1  . . .  25 - 3 . These impedance matching structures  21 - 1  . . .  21 - 3  could include one or more layers of dielectric materials that have specific and differing values for their dielectric constant, in a manner known in the art (see document 8 noted above). 
     The input reduced height waveguides  25 - 1  through  25 - 3  are connected to the modulator substrate  22  and each waveguide  25 - 1  . . .  25 - 3  is electrically coupled to a separate modulator, or modulator section,  20 - 1  . . .  20 - n  in modulator substrate  22 . Beyond the modulator substrate  22  is an, optional, output multi-furcated waveguide  26   out  which can be terminated in a high power load (not shown). In general, a wide range of optoelectronic modulator types can be used, both electro-optic (see document 6 identified above) and electro-absorptive (see document 7 identified above), as long as the top and bottom metal sides  53 ,  53   i  of each reduced height waveguide  25 - 1  . . .  25 - 3  acts as an electrode for the associated modulator element  20 - 1  . . .  20 - 3 . Between each optical modulator, or modulator section,  20 - 1  . . .  20 - n  there is an optical interconnection  30  connecting the optical modulator sections  20 - 1  through  20 - 3  in series. These interconnections  30  can be pieces of optical fiber (as depicted), or they could be integrated optic waveguides that also are contained in the same substrate  22  as the optical modulators  20 - 1  . . .  20 - 3  (as described in related U.S. patent application Ser. No. 12/141,825 mentioned above). In this way the modulators, or modulator elements,  20 - 1  through  20 - 3  are optically connected in series such that the optical signal travels sequentially from one modulator to the next (e.g., from modulator  20 - 1  to modulator  20 - 2 ). 
     In the embodiment shown in  FIGS. 9   a  and  9   b , the RF signal power is split into each of the reduced height waveguides  25 - 1  . . .  25 - 3  and proceeds toward the modulator substrate  22 . Note, however, that the electric field strength at the junction between the TEM horn  50  and the multi-furcated waveguide  25  (i.e., before the split) is the same as the electric field strength in a reduced height waveguide  25 - 1  . . .  25 - 3  (i.e., after the split). Part of each reduced height waveguide  25 - 1  . . .  25 - 3  is filled with a dielectric loading material  27 - 1  . . .  27 - 3  and part of each reduced height waveguide  25 - 1  . . .  25 - 3  is kept not filled. By varying the length of the dielectric loading layer  37 - 1  through  37 - 3  filling those reduced height waveguides  25 - 1  through  25 - 3  and/or by varying the dielectric constant of that loading material, the time it takes for the RF signal to reach the modulator substrate  22  can be adjusted for each reduced height waveguide. 
     To further describe this constraint, assume that the time it takes the RF signal to reach the modulator substrate  22  progresses by a given delay time ΔT from one reduced height waveguide to the next. In order to maintain a phase match between the RF signal arriving at each modulator and the modulation of the light reaching each modulator in sequence, the delay time ΔT preferably should meet the following constraint: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               T 
             
             = 
             
               
                 ( 
                 
                   
                     
                       L 
                       modulator 
                     
                     ⁢ 
                     
                       n 
                       modulator 
                     
                   
                   + 
                   
                     
                       L 
                       interconnect 
                     
                     ⁢ 
                     
                       n 
                       interconnect 
                     
                   
                 
                 ) 
               
               c 
             
           
         
       
     
     where L modulator  is the length of a modulator or modulator section  20 - 1  . . .  20 - 3 , L interconnect  is the length of the optical interconnect  30  (such as optical fiber) between adjacent modulator sections (e.g.,  20 - 1  and  20 - 2 ), n modulator  is the effective index of refraction of the light propagating in the integrated optic waveguide (e.g.,  23 - 1 ) of the modulator (e.g.,  20 - 1 ), n interconnect  is the effective index of refraction of the light propagating in the optical waveguide or fiber  30  that interconnects two modulators, and c is the speed of light in vacuum. The effective indices of refraction are defined to be c/v group  where v group  is the group velocity of the light propagating through the optical waveguide or the modulator. The length of the modulator preferably is limited so that the time for the optical signal to propagate completely through the modulator is no more than one-half a period of the RF signal. For example, for an RF signal frequency of 10 GHz, the optical signal preferably should propagate through the modulator in at most 0.05 nsec. Assuming a lithium niobate modulator with an effective index of refraction, n modulator =2.2 (that is, close to the index of refraction for bulk lithium niobate), the length of the modulator should be at most 
     
       
         
           
             
               L 
               modulator 
             
             = 
             
               
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     t 
                     modulator 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   • 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   c 
                 
                 
                   n 
                   modulator 
                 
               
               = 
               
                 
                   
                     
                       ( 
                       
                         0.05 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sec 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         2.998 
                         × 
                         
                           10 
                           10 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cm 
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         sec 
                       
                       ) 
                     
                   
                   2.2 
                 
                 = 
                 
                   0.68 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   cm 
                 
               
             
           
         
       
     
     Assume that the optical waveguide interconnections  30  between successive series-connected modulators also are fabricated in the lithium niobate substrate and that the length of an interconnection waveguide  30  between adjacent modulators (e.g.,  20 - 1  and  20 - 2 ) is 0.5 cm. Then the time required for the light to propagate through each interconnection is 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 t 
                 interconnect 
               
             
             = 
             
               
                 
                   
                     L 
                     
                       interconnect 
                       ⁢ 
                       
                           
                       
                     
                   
                   ⁢ 
                   • 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     n 
                     interconnect 
                   
                 
                 c 
               
               = 
               
                 
                   
                     
                       ( 
                       
                         0.5 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cm 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       2.2 
                       ) 
                     
                   
                   
                     2.998 
                     × 
                     
                       10 
                       10 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cm 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     sec 
                   
                 
                 = 
                 
                   0.037 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     nsec 
                     . 
                   
                 
               
             
           
         
       
     
     If the dielectric material loading the TEM reduced height waveguides  25 - 1  . . .  25 - 3  has a dielectric constant of 30, the desired difference between the lengths of the dielectric-filled portions  37 - 1  . . .  37 - 3  of adjacent TEM reduced height waveguides is 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       L 
                       waveguide 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     
                       ( 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             modulator 
                           
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             interconnect 
                           
                         
                       
                       ) 
                     
                     · 
                     
                       ( 
                       
                         c 
                         
                           
                             ɛ 
                             RF 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       ( 
                       
                         
                           0.05 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           nsec 
                         
                         + 
                         
                           0.037 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           nsec 
                         
                       
                       ) 
                     
                     · 
                     
                       ( 
                       
                         
                           2.998 
                           × 
                           
                             10 
                             10 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cm 
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           sec 
                         
                         
                           30 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     0.48 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cm 
                   
                 
               
             
           
         
       
     
     An alternative embodiment is shown in  FIG. 10 . In this embodiment, the delay time ΔT between the RF signals coupled from one reduced height waveguide (e.g.,  25 - 1 ) to its associated optoelectronic modulator (e.g.,  20 - 1 ) and from an adjacent reduced height waveguide (e.g.,  25 - 2 ) to its optoelectronic modulator (e.g.,  20 - 2 ) is achieved by filling those two reduced height waveguides (e.g.,  25 - 1  and  25 - 2 ) with fillers (e.g.,  37 - 1  and  37 - 2 ) comprising materials having different values for their dielectric constant (∈ 1  and ∈ 2 ). The differing values for the dielectric constant can be achieved by altering the composition of the materials that make up the dielectric filler using ways known in the art (see document 5 mentioned above). In this case, the lengths of the dielectric loaded sections (e.g.,  37 - 1  and  37 - 2 ) can be made equal, which may have an advantage with regard to ease of fabrication of the front-end assembly. This embodiment is shown as not having the optional reduced height waveguides  26 - 1  . . .  26 - 3  which would be located at the back side of the modulator substrate  22 . There preferably are impedance matching structures  21 - 1  . . .  21 - n  located between the dielectric fill portions  37 - 1  . . .  37 - 3  of each reduced height waveguide  25 - 1  . . .  25 - 3  and the horn antenna  50 , since the materials properties of these dielectric fillers could be different for each reduced height waveguide in the multi-furcation  25 . 
     Another embodiment is shown in  FIG. 11 . In that figure, optical amplifiers  35  are located in at least some of the optical interconnections  30  between the adjacent series-connected modulators (e.g.,  20 - 1  and  20 - 2 ) of modulator substrate  22 . An example of a possible optical amplifier can be found in Morito, et. al. (see document 9 mentioned above), although other types of optical amplifiers could be used. At each pass through a modulator, or modulator section, some of the power in the optical carrier may be lost (generally by scattering or absorption) or be reflected. Thus the depth of modulation that can be contributed by the subsequent modulators or modulator sections of the cascade is reduced. This embodiment would enable the optical carrier (as well as the modulation sidebands) to be amplified before the partially modulated light enters the next modulator or modulator section. Thus each modulator or modulator section of that series connection of modulators or modulator sections could contribute to the total depth of modulation in an approximately uniform manner, thereby further increasing the depth of modulation. 
       FIG. 12  shows a top view of an array of TEM horn antennas wherein each horn antenna is connected to a multi-furcated waveguide of the type shown in  FIGS. 9   a ,  9   b ,  10  and  11 . The multiple RF waveguides of the multi-furcation are coupled to multiple optoelectronic modulators, with those multiple optoelectronic modulators being optically connected in series. The optical signals coming out of the many unit elements comprising horn and multi-furcated waveguide and modulator substrate can be processed together for beam scanning at a processing unit (not shown in the figure). Different portions of the incident RF electromagnetic signal  60  are coupled into different TEM horn antennas of the array. 
       FIG. 13  shows a top view of an array of TEM horn antennas wherein each horn antenna is connected to a multi-furcated waveguide of the types shown in  FIGS. 2   a - 2   f . The multiple RF waveguides of the multi-furcation are coupled to multiple optoelectronic modulators, with those multiple optoelectronic modulators being optically connected in parallel and supplying modulated light to one or more photodetectors. The electrical signals coming out of these many unit elements comprising horn and multi-furcated waveguide and modulator substrate and photodetectors can be processed together for beam scanning at a processing unit (not shown in the figure). 
     Although TEM horn antennas are shown in  FIGS. 12 and 13 , other types of antennas also could be coupled to the multi-furcated waveguides. For example, dielectric rod antennas such as shown in  FIG. 8  could be used for the multiple antenna elements of an array. Also, the multi-furcated waveguides of the various elements of the array need not be TEM waveguides. For example, they also could be dielectric waveguides such as those shown in  FIGS. 4 ,  6   a ,  6   b  and  7 . Those dielectric waveguides could be coupled to antenna elements such as the dielectric rod antenna shown in  FIG. 8 . 
       FIG. 14  illustrates another embodiment for which a multi-furcated TEM waveguide is coupled to a modulator substrate  22  containing multiple modulators. These multiple optoelectronic modulators (not shown) can be optically connected in parallel or in series, as described above. As noted above, the multi-furcated TEM waveguide can be coupled to other kinds of antenna besides the TEM horn.  FIG. 14  shows the multi-furcated TEM waveguide  25  being coupled to a dielectric rod antenna  40 . This assembly also could include known RF transition elements such as a metal enclosed circular waveguide  41  and a circular waveguide to TEM waveguide transition  42  to improve the efficiency of the coupling of EM energy from the dielectric rod  40  to the TEM waveguide  25 . The multiple reduced height TEM waveguides  25 - 1  through  25 - n  of the multi-furcated TEM waveguide illustrated in the figure have a tapered portion  44  and a non-tapered portion  45 . The height of a reduced height waveguide, i.e., the separation between the top and bottom metal coatings of that reduced height waveguide, in a tapered portion changes from a larger value to a smaller value. This tapering further concentrates the electric field presented to the optoelectronic modulator through the reduced height waveguide. Note that all of the embodiments described above could include tapered portions of their reduced height waveguides. 
     It should be understood that the above-described embodiments are merely some possible examples of implementations of the presently disclosed technology, set forth for a clearer understanding of the principles of this disclosure. Many variations and modifications may be made to the above-described embodiments of the invention without departing substantially from the principles of the invention. All such modifications and variations are intended to be included herein within the scope of this disclosure and the present invention and protected by the following claims.