IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 21, NO. 9, SEPTEMBER 2011 507 Instantaneous Bandwidth of Counter-Phase Optical Interference Cancellation for RF Communications John Suarez, Member, IEEE, and Paul R. Prucnal, Fellow, IEEE Abstract—We describe an important second-order effect in the counter-phase optical interference cancellation system [also re- ferred to as the opto-cancellation system (OCS)]. The uniformity of signal cancellation provided by the OCS, across a nonzero instantaneous bandwidth, is limited due to mismatches in the electro-optic modulators comprising the system. The effect of these mismatches on the cancellation is examined quantitatively. Index Terms—Co-site interference cancellation, Mach–Zehnder electro-optic modulators, RF photonics, system characterization. I. INTRODUCTION T HE counter-phase method of optical interference cancel- lation allows for cancellation of interfering signals that are co-located with a receiver, allowing the receiver to detect weak signals in the presence of strong ones. Previous experi- ments have shown that the counter-phase method of optical in- terference cancellation can reduce the power of a narrowband RF signal by 70 dB, and that of a broadband additive white- Gaussian-noise (AWGN) RF signal of 96 MHz bandwidth by 30 dB, by which that reduction was approximately uniform over the full bandwidth of the AWGN signal [1], [2]. Using a second system implementation, it was shown that narrow- band-signal cancellation 80 dB was possible, and also that broadband (80 MHz) AWGN signals with center frequencies of 1–20 GHz could be cancelled down to the system noise floor [2]. The observed cancellation levels for the broadband sig- nals were 20–30 dB where, again, the cancellation was approx- imately uniform over the full signal bandwidth. This distinc- tion—and its implications—were not discussed in [1] nor [2]. In those publications, only the fundamental operation of the OCS was described. In carrying this proof-of-principle work further, however, an important nonideality was observed. If the OCS parameters were set so that a narrowband signal at one frequency (say, 500 MHz) was cancelled by 70 dB, a narrowband signal at 510 MHz would experience less cancellation with those system settings. Of course, because of the wide operational bandwidth of the OCS, the 510 MHz signal could certainly be cancelled by 70 dB; however, this was only possible if the OCS parameters were readjusted. These observations illustrate the distinction Manuscript received January 18, 2011; revised April 18, 2011; accepted June 23, 2011. Date of publication August 12, 2011; date of current version September 02, 2011. The authors are with the Department of Electrical Engineering, of Princeton University, Princeton, NJ 08544 USA (e-mail: suarezj@princeton.edu). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LMWC.2011.2163304 between the operational bandwidth and instantaneous band- width (IBW) of the OCS. This letter examines the cancellation that is instantaneously achievable by the OCS. Section II provides a description of the second-order effects which limit this cancellation, and de- velops a more general expression than was presented in [2] which takes these second-order effects into account. In Sec- tion III we present an experimental method for characterizing the instantaneous bandwidth, which is followed by additional discussion in Section IV. II. MODIFIED OCS TRANSFER FUNCTION In the introductory literature, it is often implied that the half- wave voltage of a Mach–Zehnder electro-optic modulator is a constant, as a first-order approximation. This is a reason- able assumption in certain applications, but for the cancellation operation we presently consider—in which precise matching is essential—such approximations cannot be made. The assump- tion that is a constant allows for less emphasis to be placed on modulator mismatches [5], [6]. In this way, the impression is created that deviation from a constant can always be balanced by multiplying by another constant. In fact, the present situation is more critical. The frequency variation of is indeed important, because the manner in which it varies is not precisely identical in both modulators. This mismatch is in addition to the mismatch between the modulators’ dc values of . To reiterate, it is not the frequency variation of that limits the instantaneous band- width of the OCS, but it is the mismatch in that frequency vari- ation between the two modulators, and the mismatch in the dc values of that are responsible. In this section, we will develop a system transfer function which takes these mismatches into consideration. These mismatches are considered second-order effects, since the fundamental operation of the OCS can be de- scribed without their inclusion. In [2], the transmittance function of a Mach–Zehnder electro- optic modulator is stated as (1) where is the transmittance, is the extinction, is the half-wave voltage, and is the bias point in , according to [3]. is the dc value 1 of , and is the input RF signal. Eq. (1) may be used to quantify the transmittance of either the top or bottom modulator shown in Fig. 1. Also, the output current of an externally-modulated RF photonic link can be expressed [2] as (2) 1 The notation is used to stay consistent with [4], although the notation may also be used. 1531-1309/$26.00 © 2011 IEEE