IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 9, MAY 1, 2008 733 Optical Beamforming Networks Based on Broadband Optical Source and Chirped Fiber Grating Bo Zhou, Xiaoping Zheng, Xianbin Yu, Hanyi Zhang, Yili Guo, and Bingkun Zhou Abstract—We propose a photonic beamforming network scheme based on a broadband optical source and chirped fiber grating. The principle and feasibility are proved by both theoretical anal- ysis and experiments. In 1- to 18-GHz microwave band, experi- mental results show a good delay time consistency and the ratio of signal-to-noise met the practical application demands. The time consistency errors are smaller than 1 ps in 9.25- to 10.25-GHz band. Especially, the effects of group delay ripple are effectively miti- gated compared with the tunable laser source scheme, which agree well with the theoretical results. Index Terms—Broadband optical source (BS), chirped fiber grating (CFG), microwave photonics, optical beamforming net- works (OBFNs), true-time delay (TTD). I. INTRODUCTION O PTICAL beamforming networks (OBFNs) using a pho- tonic microwave true-time delay (TTD), as one of the most important areas in microwave photonics [1], has been under intense investigation for many applications, including wideband phased-array antennas [2], broadband wireless access, and millimeter-wave radio local area networks [3]. Optical TTD networks offer many outstanding advantages over traditional electronic steering systems, such as low loss, small size, electromagnetic immunity and especially, wide instantaneous bandwidth and squint-free array steering. So far, among various TTD configurations, a dispersion-based TTD beam steerer [4]–[9] has been considered a promising technique to drive wideband microwave antennas. Chirped fiber grating (CFG) as a compact, reliable, and mature dispersion element has been used in this scenario, which can provide broadband operation and continuous spatial scanning. For example, by employing the technique of synchronal controlling multiwave- length tunable laser (TL) sources and tunable bandpass filters (TBPFs) [6], [7], or tuning the chirp of fiber grating [8], [9], the CFG-based OBFNs have been proposed and studied. However, as we know, the negative effect of group delay ripple (GDR), which is caused by the resonant nature and the manufacture imperfection of CFG, is inevitable in CFG-based systems. In this letter, we propose an OBFN scheme based on a broad- band optical source (BS) and one CFG. Such a system shows Manuscript received September 28, 2007; revised February 3, 2008. This work was supported in part by National Nature Science Foundation of China (NSFC) under Grant 6052130298 and Grant 60432020, by the 863 Project under Grant 2006AA01Z261, by the 973 Project under Grant 2006CB302805, and by Project iCHIP financed by the Italian Ministry of Foreign Affairs. The authors are with the State Key Laboratory on Integrated Optoelectronics/ Tsinghua National Laboratory for Information Science and Technology, Depart- ment of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail: zhoub02@mails.tsinghua.edu.cn; xpzheng@mail.tsinghua.edu.cn). 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/LPT.2008.921086 Fig. 1. Schematic diagram of BS-based OBFNs. RF: Radio frequency. a good delay time consistency, and especially, the effects of GDR are mitigated. The delay time deviations from linear TTD are typically within 3 ps, which are reduced more than 10 ps at 1550-nm round for 1–18 GHz compared with a TL scheme. Such a system also possesses more flexibility as well as exten- sible ability only by increasing the TBPFs at the receiver port without extra optical sources and TTD elements. II. THEORETICAL ANALYSIS The block diagram of OBFNs by employing BS is shown in Fig. 1. In general, BS is an incoherent optical source with large spectral width and white noise characteristic, and hence its output light can be regarded as an aggregate of a series of incoherent discrete optical sources with frequency interval , which can be given by the following expression: (1) where and are the power spectrum density and bandwidth of BS, respectively. and rep- resent the angle frequency and phase of equivalent discrete op- tical source, respectively, and is a random signal. Suppose that the Mach–Zehnder modulator (MZM) is driven by single radio-frequency (RF) signal ; the output optical signal can be expressed by (2) where and its Fourier transform can be expressed by . Then the modulated signals go through the CFG. When the GDR of CFG is taken into consideration, the time delay 1041-1135/$25.00 © 2008 IEEE