Abstract:
Embodiments of a photonic link having low residual carrier, for use in transmitting information between an electronic signal source and an electronic signal receiver is provided. The photonic link comprises a transmitter, which uses angle modulation, and two threshold optical frequency discriminators that are biased to provide large even-order distortion, an optical signal receiver and at least one transmission fiber to transmit complementary modulated signals between the transmitter and the optical signal receiver, whereby the optical signal receiver reconstructs the complementary modulated signals into the electronic information for acceptance by the electronic signal receiver. Exemplary methods of transmitting information are also provided.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application claims the benefit of U.S. Provisional Patent Application No. 60/710,453, filed 22 Aug. 2005, and entitled “PHOTONIC LINK USING ANGLE MODULATION AND METHOD OF USE THEREOF,” which is hereby incorporated herein by reference. 

   FIELD 
   The disclosed technology relates to photonic links for transmitting information to and from users. More specifically, the disclosed technology relates to a system and method wherein the residual optical carrier is reduced through the use of angle-modulation techniques, thus reducing both shot noise and relative-intensity noise (RIN). 
   BACKGROUND 
   Analog or microwave-photonic optical links have found widespread application in numerous sectors of communications. All modern cable-television networks use high-performance linear lasers and optical fiber to deliver the entire spectrum of analog video and subcarrier-modulated digital data to and from small groups of subscribers. See, e.g., T. E. Darcie, M. R. Phillips, “Lightwave Video Transmission,” Chapter in  Optical Fiber Telecommunications IIIA , Academic Press, NY, 1997. Other broadband access or last-mile networks, like the fiber-to-the-premises networks being deployed by telephone carriers throughout the world, also use analog optical links for transmission of broadband RF-modulated signals. See, e.g., T. H. Wood, G. C. Wilson, R. D. Feldman, J. A. Stiles, “(FTTH) system providing broad-band data over cable modems along with analog and digital video,”  IEEE Photonics Technol. Lett ., Volume 11, Issue 4, pp. 475-477 (April 1999). With the allocation of new high-frequency (e.g. 60 GHz) microwave bands for communications networks, optical links become an essential component in overcoming loss associated with coaxial or waveguide alternatives. Cellular base stations are often connected to remote antennas or groups of antennas by microwave-photonic links. See, e.g., I. Rivas, L. B. Lopes, “Transmitter macrodiversity in radio fibre microcellular networks,”  Personal, Indoor and Mobile Radio Comm., PIMRC , Vol. 3, pp. 1074-1078 (Sep. 1-4, 1997). Phased-array microwave and millimeter-wave antennas use microwave-photonic links to deliver phase reference and signal information to and from centralized processors. See, e.g., J. B. Georges, K. Y. Lau, “Broadband microwave fiber-optic links with RF phase control for phased-array antennas,”  IEEE Photonics Technol. Lett ., Vol. 5, Issue 11, pp. 1344-1346 (November 1993). In short, the transmission of microwave information as modulated optical signals through optical fiber has become an essential tool in modern communications networks. As a result, considerable work has gone into maximizing the performance of these links. See, e.g., C. H. Cox III, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,”  IEEE Trans. Microwave Theory and Techniques , vol. 38, pp. 501-509, May 1990; L. T. Nichols, K. J. Williams, and R. D. Esman, “Optimizing the ultrawide-band photonic link,”  IEEE Trans. Microwave Theory and Techniques , vol. 45, pp. 1384-1389 (August 1997). 
   Impairments introduced by microwave-photonic links (MPLs) include primarily noise and distortion. Noise limits the minimum microwave signal level that can be detected. Linearity limits the maximum microwave signal power that can be transmitted. The difference between minimum and maximum is described by the spur-free dynamic range (SFDR), one of the key figures of merit for an MPL. See, e.g., C. H. Cox, III, “Analog Optical Links: Theory and Practice,” Cambridge, 2004. Performance is measured by the ability of the optical link to preserve the fidelity of the transmitted microwave signal, as measured by parameters like the SFDR, composite-triple beat (CTB), carrier-to-noise-ratio (CNR), and link gain. Collectively, these parameters describe the ability of the link to deliver large modulated signals while minimizing noise or interference. 
   In most conventional MPLs, the intensity of a light source (directly-modulated laser or continuous-wave (CW) laser followed by an external modulator) is biased to a linear operating point, and the RF signal is applied symmetrically about this bias point to modulate the light intensity. The DC light intensity, or residual carrier, associated with this bias carries no information, but is responsible for many of the limitations of the link performance. Shot noise and relative-intensity noise (RIN), often the dominant noise sources in high-power links, result directly from the detection of this residual carrier. In systems using optical amplifiers, beating between the carrier and amplified spontaneous emission result in high levels of signal-spontaneous beat noise. Also, the available gain of the optical amplifier is consumed or saturated by this residual carrier, rather than by the desired signal. See, e.g., J. M. P. Delavaux, A Yeniay, B Neyret, C. Hullin, G. R. Wilson, “Multiple-output Er-3+ amplifier for analog and QAM distribution systems,”  Optical Fiber Communications Conference , Vol. 3., pp. WDD30-1-3 (2001). The residual carrier is subject to optical nonlinearities (stimulated Brillouin scattering (see, e.g., X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB transmission systems,”  IEEE Photonics Technol. Lett ., Vol. 4, Issue 3, pp. 287-289 (March 1992)), nonlinear refractive index (see, e.g., M. R. Phillips, T. E. Darcie, D. Marcuse, G. E. Bodeep, N. J. Frigo, “Nonlinear distortion generated by dispersive transmission of chirped intensity-modulated signals,”  IEEE Photonics Technol. Lett ., Volume 3, Issue 5, pp. 481-483 (May 1991), stimulated Raman scattering) limiting the amount of power that can be transmitted through the fiber. Finally, this residual carrier constitutes most of the power that saturates the photodetector, limiting the maximum signal power. Hence the DC bias required to operate at a linear operating point limits both the low end (noise) and high end (signal power) of the SFDR. 
   A variety (6 classes) of techniques has been proposed to mitigate the effect of the residual carrier. First, the carrier can be reduced through optical filtering. See, e.g., R. D. Esman, K. J. Williams, “Wideband efficiency improvement of fiber optic systems by carrier subtraction,”  IEEE Photonics Technol. Lett ., Vol. 7, No. 2, pp. 218-220 (February 1995). This has the same effect as increasing the modulation index (or lowering the DC bias) with commensurate increases in nonlinear distortion. 
   Second, coherent techniques have been proposed which use heterodyne detection to overcome the linearity associated with low-bias operation of a Mach Zehnder (MZ) external modulator. A. C. Lindsay, “An analysis of coherent carrier suppression for photonic microwave links,”  IEEE Trans. Microwave Theory and Tech ., Vol. 47, Issue 7, pp. 1194-1200 (July 1999). Unfortunately, the local oscillator generates noise that will offset the low-bias gain, and considerable complexity is added, including a frequency-stabilized laser that is required at the receiver. 
   Third, the bias can be modulated dynamically in response to the instantaneous magnitude of the RF envelope. See, e.g., U.S. Pat. No. 6,181,453 entitled “Method and apparatus for laser performance enhancement” and issued on Jan. 30, 2001 to T. E. Darcie and P. P. Ianonne. This can reduce the effective DC level, especially for signals with large peak factors, but the nonlinear mixing between the signal and bias modulation (the square of the signal) creates problematic third-order distortion. Also, while this approach can reduce noise from the residual carrier, the minimum average power remains substantially larger than zero, limiting the ultimate improvement. 
   Fourth, common-mode RIN (RIN present at the input to a Mach-Zehnder modulator (MZ)) can be cancelled using two fibers and a balanced photodetector. See, e.g., S. Mathai, F. Cappelluti, T. Jung, D. Novak, R. B. Waterhouse, D. Sivco, A. Y. Cho, G. Ghione, M. C. Wu, “Experimental demonstration of a balanced electroabsorption modulated microwave photonic link,”  IEEE Trans. Microwave Theory and Tech ., Vol. 49, pp. 1956-1961 (October 2001). Significant suppression of RIN has been demonstrated, but this does not affect the other challenges associated with the large residual carrier. Also, it has been shown that this technique results in reduced suppression of intensity noise for signals with larger modulation index. 
   Fifth, low-bias techniques have been explored in which an MZ is operated at lower bias than the conventional quadrature bias point (50% transmission). Unfortunately, this increases the distortion and decreases the signal, limiting the usefulness of the approach. In an attempt to reduce the distortion of this low-bias technique, an approach was explored in which 2 MZs were operated in an anti-symmetric manner with a balanced detector. See, e.g., W. K. Burns, G. K. Gopalakrishnan, R. P Moeller, “Multi-octave operation of low-biased modulators by balanced detection,”  IEEE Photonics Technol. Lett ., Volume 8, Issue 1, pp. 130-132 (January 1996). Reduction of second-order distortion was demonstrated, but maintaining the appropriate balances was challenging and overall improvement in noise was not demonstrated. The intent was to minimize second-order distortion in a low-biased link to achieve broadband operation. Hence the modulators were biased at an operating point at which the even-order distortion was small. 
   Finally, the sixth class of technique that has been proposed recently uses Class-AB techniques similar to those used in electronic amplifiers. See, e.g., C. Trask, “High efficiency broadband linear push-pull power amplifiers using linearity augmentation,”  IEEE International Symposium on Circuits and Systems, ISCAS  2002, Volume 2, pp. 11-432 to 11-435 (May 26-29, 2002). With class-AB MPLs (see, e.g., T. E. Darcie, A. Moye, P. F. Driessen, J. Bull, H. Kato, N. A. F. Jaeger, “Noise reduction in class-AB microwave-photonic links,”  IEEE Microwave Photonics  2005  Conference Proceedings , (Seoul, Korea, October 2005)), non-linear threshold electro-optic converters (NTEOCs) are used to approximately half-wave rectify the modulating signal in the output intensity modulation. Positive and negative portions of the signal are transmitted on separate but phase-matched optical paths, and recombined using a balanced photodetector. The balanced detector recreates a replica of the complete input modulated signal, and does so with close to zero DC current. Hence noise associated with the DC (or residual carrier) is minimized. A significant challenge associated with implementing Class-AB MPLs is in obtaining NTEOCs with appropriate transfer functions. Most intensity modulators have light intensity transmission-versus-voltage transfer functions that are sinusoidal. This is far from the ideal transfer function and results in a substantial departure from ideal system performance. While other approaches have been proposed, operation of a class-AB MPL with a more-suitable transfer function has not been demonstrated. 
   Other improvements have been proposed for MPLs through the use of optical angle modulation. These have attempted to overcome the nonlinearity associated with the transfer (voltage-to-transmission) of the directly- or externally-modulated source, or to cancel intensity noise. In A. Murakoshi, K. Tsukamoto, S. Komaki, “Proposal of SCM optical FM method with nonlinear compensation technique in radio on fiber link,”  Microwave Photonics,  2004,  MWP&#39; 04, 2004  IEEE International Topical Meeting , pp. 237-240 (Oct. 4-6, 2004), angle modulation of the optical carrier is used in combination with an optical filter or frequency discriminator to transmit microwave signals. The filter converts the angle modulation into amplitude modulation with potentially better linearity that an intensity-modulated system. However, this technique introduces substantial complexity and does not address the issue of noise associated with the residual carrier. In U.S. Pat. No. 6,359,716 entitled “All-optical analog FM optical receiver” and issued on Mar. 19, 2002 to Robert B. Taylor, a novel filter configuration is proposed to cancel intensity noise. This single-sideband approach is uses optical angle modulation and optical filters designed to pass both the carrier and upper or lower sidebands. As such, it does not address the issue of reduction of noise associated with the residual carrier. Coherent techniques have also been proposed in conjunction with optical frequency modulation. See, e.g., B. Cai, A. J. Seeds, “Optical frequency modulation links: theory and experiments,”  IEEE Transactions on Microwave Theory and Techniques , Volume 45, Issue 4, pp. 505-511 (April 1997). However, these add substantial complexity and do not result in commensurate performance improvement. 
   Finally, a large body of work has been produced (see, e.g., I. H. Chen, H. W. Tsao, “FM subcarrier fiber optical transmission system design and its application in next-generation wireless access,”  IEEE Journal of Lightwave Technology , Volume 16, Issue 7, pp. 1137-1148 (July 1998)) exploring the conversion of the input microwave information into an electronic frequency-modulated (FM) signal prior to transmission over a conventional MPL, exploiting the well-known robustness of FM signals to noise. However, suitable broadband modulators/demodulators to convert the input signal to an FM signal have proved difficult to produce and undesirable. Also, the large bandwidth of the resulting electronic FM signal is difficult to transmit over the MPL. 
   To summarize, there are 3 main causes of noise in a MPL: Receiver noise; shot noise; and relative intensity noise (RIN). Shot noise power increases linearly with total received power. Noise from RIN increases as the square of total received power. Receiver noise is independent of received power. While the prior art has been somewhat successful in reducing receiver noise and the effect of RIN, to date and to our knowledge, no practical method for reducing shot noise has been defined and RIN continues to be a problem. It is an object to overcome the deficiencies of the prior art. 
   SUMMARY 
   In one disclosed embodiment, a photonic link using angle modulation that has low residual carrier, for use in transmitting information between an electronic signal source and an electronic signal receiver is provided. The photonic link comprises: a transmitter to accept electronic information from the electronic signal source and to transmit optical signals, the transmitter comprising an angle-modulated optical source to convert the electronic information into an angle-modulated optical signal; and a first and second threshold optical frequency discriminator (TOFD), each TOFD biased to provide large even-order distortion; the first TOFD being complementary to the second TOFD, to provide a first and second intensity-modulated signal, the first modulated signal being complementary to the second modulated signal; and a first optical transmission network to distribute the angle-modulated optical signals from the transmitter to each of the first and second TOFD, an optical signal receiver; and a second optical transmission network to transmit the complementary intensity-modulated signals between the first and second TOFD and the optical signal receiver, whereby the optical signal receiver reconstructs the complementary modulated signals into the electronic information for acceptance by the electronic signal receiver. 
   In one aspect, the transmitter comprises an externally modulated laser. 
   In another aspect, the transmitter comprises a directly modulated laser. 
   In another aspect, the first optical transmission network comprises a power splitter and two optical paths. 
   In another aspect, the transmitter and the first and second TOFDs are co-located within a transmitter apparatus. 
   In another aspect, the receiver and the first and second TOFDs are co-located within a receiver apparatus. 
   In another aspect, the TOFDs are optical fiber Bragg-grating filters. 
   In another aspect, the first and second intensity-modulated signals are obtained by reflection from the TOFDs. 
   In another aspect the TOFDs are implemented on planar silica-based waveguides. 
   In another aspect, the first and second intensity-modulated signals are obtained by transmission through the TOFDs. 
   In another aspect, the second optical transmission network comprises two optical paths. 
   In another aspect, the second optical transmission network includes a multiplexing apparatus to combine the two intensity-modulated optical signals onto one optical path. 
   In another aspect, the optical signal receiver comprises a balanced receiver. 
   In another aspect, the balanced receiver comprises a first and a second photodetector, each having an anode and a cathode, wherein the anode of the first photodetector is connected to the cathode of the second photodetector, such that in use, the electronic information is reconstructed. 
   In another aspect, the optical transmission paths comprise free-space optical paths. 
   In another aspect, the optical transmission paths comprise optical fiber paths. 
   In another embodiment, a photonic link having low residual carrier, for use in transmitting information between an electronic signal source and an electronic signal receiver is provided. The photonic link comprises: a transmitter to accept electronic information from the electronic signal source and to transmit optical signals; the transmitter comprising a first and second non-linear threshold electronic to optical converter (NTEOC) to convert the electronic information into optical signals, the first NTEOC being complementary to the second NTEOC and wherein the NTEOC are biased to provide large even-order distortion, to provide a first and second modulated signal, the first modulated signal being complementary to the second modulated signal; the first and second NTEOC comprising an angle-modulated optical source and a first and a second TOFD; an optical signal receiver, the optical signal receiver comprising a first and a second photodetector, each having an anode and a cathode, wherein the anode of the first photodetector is connected to the cathode of the second photodetector; an optical transmission network to transmit the complementary modulated signals between the transmitter and the optical signal receiver, whereby the optical signal receiver reconstructs the complementary modulated signals into the electronic information for acceptance by the electronic signal receiver. 
   In one aspect, the optical transmission network comprises two optical paths. 
   In another aspect, the optical transmission network comprises a multiplexing apparatus to combine the first and the second modulated signals onto one optical path. 
   In another embodiment, a photonic link having low residual carrier, for use in transmitting information between an electronic signal source and an electronic signal receiver is provided. The photonic link comprises: a transmitter to accept electronic information from the electronic signal source and to transmit optical signals; the transmitter comprising an angle modulated optical source; and a first transmission path to convey the angle-modulated optical signal to a receiver apparatus; a receiver apparatus comprising a first and a second TOFD to convert the angle-modulated optical signals into intensity-modulated optical signals, the first TOFD being complementary to the second TOFD and wherein the TOFD are biased to provide large even-order distortion, to provide a first and second intensity-modulated signal, the first intensity-modulated signal being complementary to the second intensity-modulated signal; an optical balanced detector, comprising a first and a second photodetector, each having an anode and a cathode, wherein the anode of the first photodetector is connected to the cathode of the second photodetector; an optical transmission network to transmit the complementary intensity-modulated signals between the first and second TOFD and the optical balanced detector, whereby the optical balanced detector reconstructs the complementary intensity-modulated signals into the electronic information for acceptance by the electronic signal receiver. 
   In another embodiment, a method of transmitting information between an electronic signal source and an electronic signal receiver is provided comprising: accepting electronic information from the electronic signal source; angle modulating an optical source to produce an angle-modulated optical representation of the electronic information; transmitting the angle-modulated optical representation to each of two TOFDs; biasing each of two TOFDs to provide large even-order distortion; converting the angle-modulated optical representation into two complementary intensity-modulated optical signals with large even-order distortions; transmitting each of the complementary intensity-modulated optical signals to a photodetector; and reconstructing the complementary modulated signals into the electronic information for acceptance by the electronic signal receiver. 
   In one aspect of the method, the conversion is effected by TOFDs operating at a bias point such that the square root of the variance of the modulated optical signal frequency spectrum is greater than the difference between the carrier frequency and the threshold frequency of the TOFC. 
   In another aspect of the method, the conversion is effected by TOFDs operating at a bias point that provides a normalized modulation index of greater than approximately 0.7. 
   In another aspect of the method each of the TOFDs are operating with a threshold frequency that corresponds to less than approximately 25% maximum transmission towards the photodetector. 
   In another aspect of the method, each of the modulators are operating at a bias point of less than approximately 15% maximum transmission towards the photodetector. 
   In another aspect of the method, the angle modulation is implemented using a continuous-wave laser source and a phase modulator. 
   In another aspect of the method, the angle modulation is implemented using a directly-modulated laser diode. 
   In another aspect the method further comprises multiplexing to combine the complementary intensity-modulated optical signals for transmission on one transmission fiber. 
   In another aspect the method further comprises optical amplification. 
   In another embodiment, a photonic link having low residual carrier, for use in transmitting information between an electronic signal source and an electronic signal receiver is provided. The photonic link comprises: a transmitter to accept electronic information from the electronic signal source and to transmit optical signals, the transmitter comprising an angle-modulated optical source to convert the electronic signals into an optical angle-modulated representation; a TOFD to convert the angle modulated optical representation into an intensity-modulated optical signal, and wherein the TOFD is biased to provide large even-order distortion and in which the converter is biased such that the normalized modulation index exceeds 1; a first transmission path to convey the optical angle-modulated representation to the TOFD; an optical signal receiver; and a second optical transmission path to transmit the intensity-modulated optical signals between the TOFD and the optical signal receiver, whereby the optical signal receiver reconstructs the electronic information for acceptance by the electronic signal receiver, and in which the reconstructed electronic information contains large even-order distortion. 
   In one aspect, the first optical transmission path comprises a free-space optical path. 
   In another aspect, the second optical transmission path comprises a free-space optical path. 
   In another aspect, the first optical transmission path comprises an optical fiber. 
   In another aspect, the second optical transmission path comprises an optical fiber. 
   In another aspect, the information accepted from an electronic signal source extends over a band of frequencies such that the maximum frequency is less than twice the minimum frequency, rendering all even-order distortion products outside of the band of interest. 
   In yet another embodiment a method of transmitting information between an electronic signal source and an electronic signal receiver is provided comprising: accepting electronic information from the electronic signal source; angle modulating an optical carrier with the electronic information to obtain a optical angle-modulated representation of the electronic information; transmitting the optical angle-modulated representation to a TOFD; biasing the TOFD to provide large even-order distortion and a normalized modulation index exceeding 1; converting the optical angle-modulated representation into an optical intensity-modulated signal with large even-order distortions; transmitting the intensity-modulated optical signal to an optical receiver; and reconstructing the intensity-modulated optical signal into the electronic information for acceptance by the electronic signal receiver. 
   In one aspect of the method one of the optical signals are transmitted by a free-space optical path. 
   In another aspect of the method, the information being transmitted extends over a band of frequencies such that the maximum frequency is less than twice the minimum frequency, rendering all even-order distortion products outside of the band of interest. 
   The foregoing and other objects, features, and advantages of the invention will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic block diagram of a Class-AB photonic link in accordance with the prior art, based on the use of external modulators. 
       FIGS. 2(A) and 2(B)  are graphs describing the construction of the effective transfer function for class AB operation using intensity modulators, in accordance with the prior art. 
       FIG. 3  is a schematic block diagram showing a laser that is externally phase modulated and separated into two paths at the transmitter, in accordance with an embodiment of the disclosed technology. 
       FIG. 4  is a schematic block diagram showing a photonic link in which the angle-modulated signal is sent over one optical path and separated into complementary signals at the receiver, in accordance with an embodiment of the disclosed technology. 
       FIG. 5  is a schematic block diagram showing a photonic link that uses a single optical path in an unbalanced configuration in accordance with an embodiment of the disclosed technology. 
       FIG. 6  is a graph describing the ideal transfer function for the threshold optical frequency discriminators, in accordance with an embodiment of the disclosed technology. 
       FIG. 7  defines a method for quantifying the operational difference between the invention and prior art, in terms of modulation conditions applied to each nonlinear threshold electric-to-optic converter. 
   

   DETAILED DESCRIPTION 
   As used in this application and in the claims, the singular forms “a,” “an,” and “the” include the plural forms unless the context clearly dictates otherwise. Furthermore, the term “microwave information” refers to any form of microwave, millimeter wave, or analog radio-frequency signal. The term “threshold optical frequency discriminator (TOFD)” refers to an optical filter with a transmission-versus-frequency characteristic that exhibits a sharp turn on or threshold. The term “nonlinear threshold electrical-to-optical (E-O) converter (NTEOC)” refers to a device that has a light-output-versus-current (or voltage) transfer function that, when biased in the vicinity of the threshold, approximately half-wave rectifies an input microwave signal. Examples include laser diodes, externally modulated optical sources using Mach-Zehnder modulators or Electro-absorption modulators, and angle-modulated (frequency or phase) optical sources in conjunction with a threshold optical frequency discriminator (TOFD). The term “complementary converters or paths” refers to a pair of approximately identical converters or paths wherein the transfer function of one is inverted relative to the other with respect to the polarity of the input microwave information or the optical frequency relative to the optical carrier. The term “directly-modulated laser diode” refers to a laser diode or injection-locked laser diode that is intensity- or angle-modulated by modulation of applied current. The term “externally-modulated laser” refers to a laser operated by continuous-wave pumping but intensity- or angle-modulated using an external device such as a Mach-Zehnder (MZ) electro-optic modulator, electro-absorption modulator, or phase modulator. The term “optical communications path” refers to a single optical fiber or free-space optical connection between a transmitter and receiver. The term “balanced detector” refers to a pair of closely-matched photodetectors with the anode of one connected electrically to the cathode of the other, with the output signal taken from this junction. 
   In order to describe the operation of the disclosed angle-modulated (AM) Class-AB (AM-CAB) techniques for MPLs, we begin with a review of the prior art of intensity-modulated Class-AB (IM-CAB) techniques. With IM-CAB (see T. E. Darcie, A. Moye, P. F. Driessen, J. Bull, H. Kato, N. A. F. Jaeger, “Noise reduction in class-AB microwave-photonic links,”  IEEE Microwave Photonics  2005  Conference Proceedings  (Seoul, Korea, October 2005)), non-linear threshold electro-optic converters (NTEOCs) are used to ideally half-wave rectify the modulating signal in the output intensity modulation. Positive and negative portions of the signal are transmitted on separate but phase-matched (with respect to the microwave signal) optical paths, and recombined using a balanced photodetector, as illustrated in  FIG. 1 . An optical carrier generated by optical source  11  is split into two equal portions by coupler  13  and delivered to two complementary optical modulators  14  and  15 . These are biased to appropriate operating points by voltage or current sources  18  and modulated about these bias points by the input microwave signal. Coupler  16  is used to provide identical modulation signals for each of the modulators  14 ,  15 , and a phase controller  17  is used to control the relative phase of the modulating signals reaching the two modulators  14 ,  15 . The coupler, modulators and phase controller components collectively comprise the transmitter  10 . 
   An optical transmission path  50 , comprised of first and second transmission fibers  51  and  52 , deliver the complementary modulated signals to an optical signal receiver  70 . This receiver  70  is a balanced photodetector consisting of two photodetectors, a first photodetector  71  and a second photodetector  72  with the anode of either the first  71  or second photodetector  72  connected to the cathode of the other photodetector. At this common junction, photocurrent generated in either the first  71  or second photodetector  72  is subtracted from that generated in the other photodetector, resulting in reconstruction of the original microwave signal as an output microwave signal to be received by an electronic signal receiver. The balanced detector recreates a replica of the complete input modulated signal, and does so with close to zero DC current. Hence noise associated with the DC (or residual carrier) is minimized. 
   A significant challenge associated with implementing Class-AB MPLs is in obtaining NTEOCs with appropriate transfer functions. Most intensity modulators are based on the MZ, and therefore have light intensity transmission-versus-voltage transfer functions that are sinusoidal. This is far from the ideal transfer function and results in a substantial departure from ideal system performance. Electro-absorption modulators have transfer functions that may have advantages over MZ, but these are generally limited in output power relative to MZ-based approaches. Direct laser modulation has the benefit of low cost, small size, and low power consumption. While simple in principle, several challenges must be overcome. Relative intensity noise (RIN) from lasers that can be directly-modulated (e.g. distributed feedback (DFB) lasers) tends to be high when operated only slightly above threshold. Also, the impedance of each laser diode, as seen by the microwave source, is a function of the laser bias. In the vicinity of the laser threshold current, the positive-negative junction begins to conduct, making a transition from an open circuit to a relatively low-impedance (a few ohms) at currents well above threshold. This raises challenges in designing a drive circuit for the pair of Class-AB lasers that will not induce additional signal distortion. Finally, lasers operated at low bias currents are subject to nonlinear distortion referred to as resonance distortion that results from photon-carrier dynamics within the laser diode. This distortion is exacerbated by the low resonance frequency associated with the low bias current. 
   One feature of the modulated optical sources is that they exhibit substantially nonlinear or threshold behavior in the light-versus-voltage (or current) turn-on characteristics (or transfer function). Devices operated in this mode will be referred to as non-linear threshold electrical-to-optical (E-O) converters (NTEOC). This is generally the case for appropriately-biased directly-modulated lasers, and is approximately the case for appropriately-biased external modulators. The ideal transfer function for a NTEOC for IM-CAB applications is shown in  FIG. 2B , in comparison with a similar device operated in a conventional manner. In conventional use, as shown in  FIG. 2A , the bias point is high enough that modulation induced by the RF input creates a replica of the RF input in the modulated output optical intensity. This results in penalties arising from the DC bias point or residual carrier. In  FIG. 2B , however, two devices are operated in a complementary manner, with each biased so as to provide only half of the modulated output signal. What is delivered into the first transmission fiber  51  from NTEOC  14  ( FIG. 1 ) is essentially zero light for voltage (or current) below threshold, and a light intensity that is essentially linearly proportional to voltage above threshold. This is reversed for the complementary modulated source  15  that delivers modulated optical power into the second transmission fiber  52 . Note that the complement can be realized by inverting the RF signal, and does not require design of a physically distinct NTEOC. It can be seen that the result of the subtraction in the optical signal receiver  70  is to create an effective transfer function for the link that is shown in  FIG. 2B . Modulation by the input microwave signal about the bias point impresses one half of the half-wave-rectified microwave signal onto the light intensity in one transmission fiber  51 , and the opposite half to the other transmission fiber  52 . The result is a linear transfer function with zero average bias (or residual carrier). 
   It has been predicted that if the ideal NTEOC can be realized, substantial performance improvement can be realized. For a single modulating microwave carrier with a 10% modulation index, the shot noise is reduced by approximately 12 dB, relative to the shot noise in a conventional link. Likewise, intensity noise, which scales as the square of the received total power, is reduced by approximately 20 dB. Also, since the carrier is not present, more signal power can be launched into the transmission fibers  51 ,  52  or detected by the photodetectors  71 ,  72  before fiber nonlinearity or saturation becomes a problem. Hence substantial improvements in link performance can be achieved. However, achieving the ideal NTEOC with IM-CAB is difficult. 
   The present application discloses systems and methods to obtain nearly-ideal NTEOC function through the use of angle modulation (frequency or phase) of the optical carrier and novel optical filtering techniques using what will be referred to as a threshold optical frequency discriminator (TOFD). An example of this system is described in  FIG. 3 . A transmitter  100  is connected to a receiver  70  through two optical fibers  51  and  52 , generally referred to as optical paths. The transmitter  100  includes an angle modulated laser  20  consisting of a laser  21  and an angle modulator  22 , and coupler  13 , also referred to as a power splitter, two optical circulators  16  and a set of complementary optical filters  14 ,  15 . Microwave information is applied to modulator  22  to modulate either the frequency or phase of the signal emitted from the laser  21 . This angle-modulated signal is split into two equal portions by a coupler  13 . In this example, TOFDs  14 ,  15  reflect a portion of the input optical frequencies back through the circulators  16  to second couplers  32 . Each coupler  32  samples a small portion of these signals for detection in photodetectors  31 . The electronic signals generated by the detectors are used by controllers  30  to maintain the appropriate frequency position of the TOFDs with respect to the optical source frequency. The majority of the signals reflected from the TOFDs are passed through optical fibers  51 ,  52  to receiver  70 . As with IM-CAB, this receiver  70  is a balanced photodetector consisting of two photodetectors, a first photodetector  71  and a second photodetector  72  with the anode of either the first  71  or second photodetector  72  connected to the cathode of the other photodetector. At this common junction, photocurrent generated in either the first  71  or second photodetector  72  is subtracted from that generated in the other photodetector, resulting in reconstruction of the original microwave signal as an output microwave signal to be received by an electronic signal receiver. 
   A variety of suitable angle modulators are available.  FIG. 3  shows an un-modulated laser that is externally angle-modulated. This modulator would generally be a phase modulator made using electro-optic waveguides in materials such as Gallium Arsenide, or Lithium Niobate. Phase modulation has recently been demonstrated using waveguides based on Silicon. Alternatively, the angle-modulated optical source could be a diode laser that is directly frequency-modulated (or chirped) by applied modulation current. Numerous examples of compact tunable semiconductor laser sources have been propose and demonstrated, any of which could serve as the angle-modulated source. 
   It may also be desirable to recombine the two signals leaving couplers  32  into fibers  51 ,  52  by using a well-known multiplexing technique such as wavelength-division multiplexing or polarization combining, such that the two optical fibers  51 ,  52  can be replaced with a single transmission fiber. A suitable demultiplexor would then be inserted prior to receiver  70  to recreate the two inputs to detectors  71 ,  72 . 
   An alternative embodiment of the present invention is shown in  FIG. 4 . Rather than creating two optical paths and placing the TOFDs in the transmitter ( FIG. 3 ), the splitting and filtering operations are implemented at the receiver. The functions and numbering of the components now in receiver  70  are identical to those described above for  FIG. 3 . An advantage of  FIG. 4  over  FIG. 3  is that only one transmission path is required. Complexity is concentrated in the receiver, which may be an advantage or disadvantage depending on specifics of the application. A disadvantage is that the optical power levels in the fiber are higher, and may include some residual carrier (if the modulation index of the angle modulation is low). While this residual carrier will not be detected in detectors  70 ,  71 , it may contribute to nonlinear effects in the transmission fiber  52 . 
   Another embodiment of the invention is shown in  FIG. 5 , in which only one half of the balanced configuration of  FIG. 4  is used. This could also be implemented with the TOFD at the transmitter, in accordance with  FIG. 3 . In this case, only signals corresponding to one polarity of the input microwave signal are detected. This reduces the detected RF signal power by 6 dB relative to the configuration of  FIGS. 3 and 4 , but also reduces the shot noise by 3 dB and simplifies the system substantially. It also results in a received signal that has high even-order nonlinear distortion, but this may be acceptable for a wide variety of applications wherein the microwave signal spectrum to be transmitted occupies only a narrow range of frequencies. While it has been demonstrated [ 18 ] that the use of FM modulation and a single optical filter or frequency discriminator can be used (in place of the TOFD) for MPLs, this has been done with a bias point that corresponds to a high average residual carrier. The use of TOFD with a shape described below and the alignment of the optical carrier frequency close to the threshold of the TOFD has not been suggested, and leads to significant reduction in overall noise along with the other advantages associated with the elimination of the residual carrier. 
   The key to successfully minimizing the detected residual carrier with FM-CAB is in the structure of the TOFDs  14 ,  15 . These are designed to provide transmission-versus-frequency characteristics in accordance with  FIG. 6 . TOFD A has maximum transmission (or reflectivity) for optical frequencies less than f A max  and zero transmission (or reflectivity) for frequencies greater than f C . Between these two frequencies, the transmission (or reflectivity) of optical intensity is a linear function of the optical frequency. TOFD B has the inverse characteristic, as shown. Both filters are adjusted by well-known tuning mechanisms (angle, temperature, strain, etc.) such that the frequency of the un-modulated optical carrier coincides with the common f C . 
   Operation of the link can be understood by considering a simple time-domain representation of a frequency-modulated (FM) signal, in which the instantaneous optical frequency is linearly proportional to the applied signal voltage. Assuming that the input microwave information has zero mean voltage (capacitively coupled, as is generally the case for microwave circuits), positive portions of the signal will result in optical frequencies greater than f C  by an amount proportional to the voltage. TOFD B will pass these signals with intensity proportional to the instantaneous optical frequency, which is in turn proportional to the input voltage. Hence the output of TOFD B is ideally a half-wave rectified (positive half) replica of the input voltage. Similarly, the output of TOFD A is a half-wave rectified (negative half) replica of the input voltage. Since the photodetection process can only detect positive optical power, the balanced receiver subtracts one of these from the other, resulting in a complete reconstruction of the input microwave signal, while minimizing the detected DC photocurrent. A more rigorous treatment of the approach using spectral analysis reveals subtleties and detailed quantitative results, but does not affect the operating principles disclosed herein. 
   It is desirable to have as close to the ideal transfer functions described in  FIG. 6  as possible. Sharp turn on at f C  and high linearity of the optical discriminator (sloping portion of the TOFD shape) are desirable features. In addition, the phase response, as measured by the group delay, of the filters are desirably constant over the sloping portions. Otherwise, frequency dependence of the group delay will interact with effects such as chromatic dispersion to create nonlinear distortion in the output signals. Note that it may also be possible to alter the phase response to compensate for system-related impairments such chromatic dispersion of the transmission fiber. 
   A variety of filter technologies can be used to approximate suitable TOFD characteristics. These include thin film or interference filters, filters integrated on silicon-based optical waveguides, and fiber Bragg-grating filters. We have specified and had manufactured using standard fabrication techniques fiber Bragg-grating filters that provide nearly ideal characteristics. These devices provide a means of implementing CAB techniques using angle modulation with in a manner that provides almost ideal performance, while attempts to implement IM-CAB have been limited by the lack of ideal NTEOC. See, e.g., T. E. Darcie, A. Moye, P. F. Driessen, J. Bull, H. Kato, N. A. F. Jaeger, “Noise reduction in class-AB microwave-photonic links,”  IEEE Microwave Photonics  2005  Conference Proceedings  (Seoul, Korea, October 2005). It is the combined interaction of the angle-modulated laser source and each TOFD that makes an NTEOC. 
   We have used the term angle modulation to represent both frequency (FM) and phase modulation (PM), which is common practice within the art. It is well known that the instantaneous frequency is the derivative of the phase. For typical narrowband microwave applications, in which the microwave signals occupy a small range of frequencies ΔΩ relative to the center frequency Ω, the relationship between FM and PM is straightforward. For example, for a phase modulated optical signal of the form E(t)=E O  cos(ω O t+kV(t)), where the modulating microwave signal is of the form V(t)=V O  cos(Ωt), the instantaneous optical frequency ω is derivative of the phase term ω O t+kV(t) which is equal to ω O −kV O Ω sin Ωt. Hence PM results in what can be described as FM with peak frequency deviation kV O Ω and a 90 degree phase shift. For narrowband applications, the difference introduced by the dependence of the frequency deviation on Ω is minor. If needed, the dependence of the FM frequency deviation on Ω can be compensated for using standard equalization techniques. Therefore, we can use FM and PM interchangeably, and recognize that standard techniques can be employed to convert between one and the other. 
   Under conditions of ideal balance between the two complementary paths  14  to  71  and  15  to  72 , the even-order distortion generated by each TOFD ( 14 ) would be exactly cancelled by that of the other (15). The Class-AB approach is then capable of operation over a broad RF bandwidth (for example, 2-20 GHz) over which even-order distortion products must be tolerated. However, it is realized that substantial even-order distortion will be generated by each TOFD, and that exact cancellation will be difficult. For applications with small fractional bandwidths (for example, 5-10 GHz, or 19-20 GHz), all even-order distortion falls outside of the band of interest, and balancing is far less critical. The single-TOFD approach described in  FIG. 5  is applicable to small fractional bandwidths only. 
   Since the term “half-wave rectified” is somewhat subjective, it is useful to define means to quantify the degree of nonlinear rectification occurring in the TOFD-based NTEOC.  FIG. 7  shows the transfer function of a TOFD with a sharp threshold. Under conditions where half-wave rectification were not desired, the TOFD would be biased (tuned to a frequency relative to the optical carrier frequency) that is sufficiently high that the addition of modulating microwave signal (voltage) and corresponding angle modulation creates a reasonably accurate replica of the microwave signal in light output. As the magnitude of the modulating signal increases, the excursion of the optical frequency on the low-frequency side of the optical carrier may be driven below the discriminator threshold, resulting in clipping of the light output, as shown in  FIG. 7 . 
   For arbitrary forms of microwave input signals, the probability of clipping in the TOFD can be seen in  FIG. 7  from the overlap between the probability density function (PDF) of the optical frequency S(f) (which is linearly proportional to the input microwave signal voltage for FM), and the TOFD transfer function, as shown in  FIG. 6 . Distribution S(f) may take on a variety of forms depending on the form of the input microwave signal. The expected value can be defined as
 
 E ( f   2 )=∫ −∞   +8   f   2   S ( f ) df  
 
   a simple quantity representative of the statistical range of frequencies contained within the optical signal frequency-modulated by the microwave signal. If the input signal consists of a large number (N) of equal-amplitude sinusoidal signals, this PDF becomes a Gaussian distribution with standard deviation σ 2 , where σ is given by σ=kV p √{square root over (N/2)}. N is the number of channels, V p  is the peak voltage for one channel, and k is the proportionality constant between the input microwave voltage and optical frequency. That is, a change input voltage of 1 volt results in a change in optical frequency of k GHz. In a conventional link, the ratio of σ to the difference between bias and threshold frequencies of the TOFD is rarely greater that 0.4 (roughly as shown in  FIG. 7 ). Since the difference between frequency of the optical carrier and the threshold of the TOFD translates directly to the average light output, and a translates directly to the square root of the variance of the light output (intensity modulation), this ratio is equivalent to the well-known normalized modulation index μ. In the ideal (Class B) embodiment, the carrier frequency is equal to the threshold frequency. Therefore, μ becomes infinite. This corresponds to ideal half-wave rectification of the signal S(f) during conversion to modulated optical power. For non-ideal (class AB) some offset between carrier frequency and TOFD threshold bias voltage is used. While it is desirable to operate each of the complementary NTEOCs as close to half-wave rectification as possible, other practical concerns may prevent this. Therefore, a way to distinguish Class-AB operation from conventional operation is to define Class AB as operation in which each NTEOC is operated with μ greater than approximately 0.7. By using μ, this metric can be applied to all forms of TOFD transfer functions. Alternatively, one could define Class-AB as operation with modulation conditions for which σ is greater than the difference between the bias point and the threshold point. 
   Once the complementary optical signals have been generated at the outputs of each NTEOC, several configurations can be used to convey the signals to the photodetectors. A simple solution is to use two separate optical fibers  51  and  52 , one for each signal, as defined in  FIG. 3 . This method is already used in conventional links where intensity noise is cancelled using a dual-output MZ. Alternatively, the two signals can be combined for transmission along a single fiber, then separated prior to the two detectors. The methods for combining could include, but are not limited to wavelength-division multiplexing, polarization multiplexing, and in principle, time-division multiplexing. 
   For single or dual-fiber implementations, the phases of the two received signals are desirably aligned. This can be done by adjusting or controlling the fiber lengths. Optical delay lines are available from many suppliers that enable fine tuning of the fiber length. Alternatively, the phase of the microwave signals can be adjusted after the photodetectors but before combining in the receiver. 
   Free-space communications could also benefit from the reduced noise achieved with Class-AB techniques. In this case, the optical fiber  50  or fibers  51 ,  52  of the optical transmission path  50  would be replaced with free-space optical path(s) between telescopes or lenses. The same considerations apply to single or dual-path approaches. Phase alignment can be done by varying the phase of the microwave signal, or by adjusting the optical path length. 
   Detection can be implemented using a balanced receiver  70 , which subtracts the photocurrent generated in one detector directly from that generated in the other. Alternatively, two separate detectors  71  and  72  can be used, and the output of one inverted relative to the other prior to or during combining of the microwave signals. This can be done using a variety of microwave devices including 180 degree hybrids, inverters, and 90 degree hybrids. Any type of detector can be used, including PiN photodiodes, avalanche photodetectors, or MSM detectors. 
   The foregoing is a description of several embodiments of the invention. As would be known to one skilled in the art, variations that do not vary the scope of the invention are contemplated. For example, the angle-modulated optical source could be any source that allows frequency or phase of an optical carrier to be modulated in response to a microwave input. Optical amplification may be used to increase optical signal power at any point within the optical link. A variety of numerous microwave techniques may be employed to assist in creating an accurate or economical microwave circuit implementation. 
   In view of the many possible embodiments to which the principles of the disclosed invention may be applied, it should be recognized that the illustrated embodiments are only preferred examples of the invention and should not be taken as limiting the scope of the invention. Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims.